Product metric: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search

en>HMSSolent

en>David Eppstein
Remove orphan tag, this time for sure
 
en>HMSSolent
m Reverted 1 edit by 103.24.88.34 identified as test/vandalism using STiki
 
Line 1: Line 1:
The writer is known as Araceli Gulledge. What he truly enjoys doing is to perform handball but he is struggling to find time for it. Her family lives in Idaho. The job I've been occupying for years is a bookkeeper but I've already utilized for another one.<br><br>Feel free to surf to my web page: [http://Appbutton.co.kr/vp/xe/vp/248180 auto warranties]
{| align=right class=wikitable width=300
|+ Graphs of three [[List of regular polytopes#Nine Dimensions|regular]] and related [[uniform polytope]]s
|-
| || || || || || || || || || ||
|- align=center valign=top
|colspan=6|[[File:9-simplex t0.svg|150px]]<br />[[9-simplex]]
|colspan=6|[[File:9-simplex t1.svg|150px]]<br />[[Rectified 9-simplex]]
|- align=center valign=top
|colspan=6|[[File:9-simplex t01.svg|150px]]<br />[[Truncated 9-simplex]]
|colspan=6|[[File:9-simplex t02.svg|150px]]<br />[[Cantellated 9-simplex]]
|- align=center valign=top
|colspan=6|[[File:9-simplex t03.svg|150px]]<br />[[Runcinated 9-simplex]]
|colspan=6|[[File:9-simplex t04.svg|150px]]<br />[[Stericated 9-simplex]]
|- align=center valign=top
|colspan=6|[[File:9-simplex t05.svg|150px]]<br />[[Pentellated 9-simplex]]
|colspan=6|[[File:9-simplex t06.svg|150px]]<br />[[Hexicated 9-simplex]]
|- align=center valign=top
|colspan=6|[[File:9-simplex t07.svg|150px]]<br />[[Heptellated 9-simplex]]
|colspan=6|[[File:9-simplex t08.svg|150px]]<br />[[Octellated 9-simplex]]
|- align=center valign=top
|colspan=6|[[File:9-orthoplex.svg|150px]]<br />[[9-orthoplex]]
|colspan=6|[[File:9-cube.svg|150px]]<br />[[9-cube]]
|- align=center valign=top
|colspan=6|[[File:Truncated 9-orthoplex.png|150px]]<br />[[Truncated 9-orthoplex]]
|colspan=6|[[File:Truncated 9-cube.png|150px]]<br />[[Truncated 9-cube]]
|- align=center valign=top
|colspan=6|[[File:Rectified enneacross.png|150px]]<br />[[Rectified 9-orthoplex]]
|colspan=6|[[File:Rectified 9-cube.png|150px]]<br />[[Rectified 9-cube]]
|- align=center valign=top
|colspan=6|[[File:9-demicube.svg|150px]]<br />[[9-demicube]]
|colspan=6|[[File:Truncated 9-demicube.png|150px]]<br />[[Truncated 9-demicube]]
|}
In nine-dimensional [[geometry]], a '''polyyotton''' (or '''9-polytope''') is a [[polytope]] contained by 8-polytope facets. Each [[7-polytope]] [[Ridge (geometry)|ridge]] being shared by exactly two [[8-polytope]] [[Facet (mathematics)|facets]].
 
A '''uniform polyyotton''' is one which is [[vertex-transitive]], and constructed from [[uniform polyzetton|uniform]] [[Facet (geometry)|facets]].
 
A [[5-polytope#A note on generality of terms for n-polytopes and elements|proposed name]] for 9-polytope is '''polyyotton''' (plural: '''polyyotta'''), created from ''poly-'', ''[[yotta|yotta-]]'' (a variation on [[Numerical prefix|octa]], meaning eight) and ''-on''.
 
== Regular 9-polytopes ==
 
Regular 9-polytopes can be represented by the [[Schläfli symbol]] {p,q,r,s,t,u,v,w}, with '''w''' {p,q,r,s,t,u,v} 8-polytope [[Facet (mathematics)|facets]] around each [[Peak (geometry)|peak]].
 
There are exactly three such [[List of regular polytopes#Convex 4|convex regular 9-polytopes]]:
# {3,3,3,3,3,3,3,3} - [[9-simplex]]
# {4,3,3,3,3,3,3,3} - [[9-cube]]
# {3,3,3,3,3,3,3,4} - [[9-orthoplex]]
 
There are no nonconvex regular 9-polytopes.
 
== Euler characteristic ==
 
The [[Euler characteristic]] for 9-polytopes that are topological [[8-sphere]]s (including all convex 9-polytopes) is zero. χ=V-E+F-C+f<sub>4</sub>-f<sub>5</sub>+f<sub>6</sub>-f<sub>7</sub>+f<sub>8</sub>=2.
 
== Uniform 9-polytopes by fundamental Coxeter groups ==
 
Uniform 9-polytopes with reflective symmetry can be generated by these three Coxeter groups, represented by permutations of rings of the [[Coxeter-Dynkin diagram]]s:
 
{| class=wikitable
!colspan=2|[[Coxeter group]]
![[Coxeter-Dynkin diagram]]
|-
||A<sub>9</sub>|| [3<sup>8</sup>]||{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
|-
||B<sub>9</sub>||[4,3<sup>7</sup>]||{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
|-
||D<sub>9</sub>||[3<sup>6,1,1</sup>]||{{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|3|node|3|node}}
|}
 
Selected regular and uniform 9-polytopes from each family include:
* [[Simplex]] family: A<sub>9</sub> [3<sup>8</sup>] - {{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
** 271 uniform 9-polytopes as permutations of rings in the group diagram, including one regular:
**# {3<sup>8</sup>} - [[9-simplex]] or '''deca-9-tope''' or '''decayotton''' - {{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
* [[Hypercube]]/[[orthoplex]] family: B<sub>9</sub> [4,3<sup>8</sup>] - {{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
** 511 uniform 9-polytopes as permutations of rings in the group diagram, including two regular ones:
**# {4,3<sup>7</sup>} - [[9-cube]] or '''enneract''' - {{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}
**# {3<sup>7</sup>,4} - [[9-orthoplex]] or '''enneacross''' - {{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node|4|node}}
* [[Demihypercube]] D<sub>9</sub> family: [3<sup>6,1,1</sup>] - {{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|3|node|3|node}}
** 383 uniform 9-polytope as permutations of rings in the group diagram, including:
**# {3<sup>1,6,1</sup>} - [[9-demicube]] or '''demienneract''', '''1<sub>6,1</sub>''' - {{CDD|nodes_10|split2|node|3|node|3|node|3|node|3|node|3|node|3|node}}; also as h{4,3<sup>8</sup>} {{CDD|node_h|4|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}.
**# {3<sup>6,1,1</sup>} - [[9-orthoplex]], '''6<sub>1,1</sub>''' - {{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}
 
== The A<sub>9</sub> family ==
 
The A<sub>9</sub> family has symmetry of order 3628800 (10 factorial).
 
There are 256+16-1=271 forms based on all permutations of the [[Coxeter-Dynkin diagram]]s with one or more rings. These are all enumerated below. Bowers-style acronym names are given in parentheses for cross-referencing.
 
{| class="wikitable"
!rowspan=2|#
!rowspan=2|Graph
!rowspan=2|[[Coxeter-Dynkin diagram]]<br />[[Schläfli symbol]]<br />Name
!colspan=9|Element counts
|-
|| 8-faces|| 7-faces|| 6-faces|| 5-faces|| 4-faces|| Cells|| Faces|| Edges|| Vertices
|-
|- align=center
!1
|[[File:9-simplex t0.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}<br />t<sub>0</sub>{3,3,3,3,3,3,3,3}<br />[[9-simplex]] (day)
|10||45||120||210||252||210||120||45||10
|- align=center
!2
|[[File:9-simplex t1.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}<br />t<sub>1</sub>{3,3,3,3,3,3,3,3}<br />[[Rectified 9-simplex]] (reday)
|| || || || || || || ||360 ||45
|- align=center
!3
|[[File:9-simplex t2.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node}}<br />t<sub>2</sub>{3,3,3,3,3,3,3,3}<br />[[Birectified 9-simplex]] (breday)
|| || || || || || || ||1260 ||120
|- align=center
!4
|[[File:9-simplex t3.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node}}<br />t<sub>3</sub>{3,3,3,3,3,3,3,3}<br />[[Trirectified 9-simplex]] (treday)
|| || || || || || || ||2520 ||210
|- align=center BGCOLOR="#e0f0e0"
!5
|[[File:9-simplex t4.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node}}<br />t<sub>4</sub>{3,3,3,3,3,3,3,3}<br />[[Quadrirectified 9-simplex]] (icoy)
|| || || || || || || ||3150 ||252
|- align=center
!6
|[[File:9-simplex t01.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1</sub>{3,3,3,3,3,3,3,3}<br />[[Truncated 9-simplex]] (teday)
|| || || || || || || ||405 ||90
|- align=center
!7
|[[File:9-simplex t02.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2</sub>{3,3,3,3,3,3,3,3}<br />[[Cantellated 9-simplex]]
|| || || || || || || ||2880 ||360
|- align=center
!8
|[[File:9-simplex t12.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}<br />t<sub>1,2</sub>{3,3,3,3,3,3,3,3}<br />[[Bitruncated 9-simplex]]
|| || || || || || || ||1620 ||360
|- align=center
!9
|[[File:9-simplex t03.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3</sub>{3,3,3,3,3,3,3,3}<br />[[Runcinated 9-simplex]]
|| || || || || || || ||8820 ||840
|- align=center
!10
|[[File:9-simplex t13.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}<br />t<sub>1,3</sub>{3,3,3,3,3,3,3,3}<br />[[Bicantellated 9-simplex]]
|| || || || || || || ||10080 ||1260
|- align=center
!11
|[[File:9-simplex t23.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}<br />t<sub>2,3</sub>{3,3,3,3,3,3,3,3}<br />[[Tritruncated 9-simplex]] (treday)
|| || || || || || || ||3780 ||840
|- align=center
!12
|[[File:9-simplex t04.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,4</sub>{3,3,3,3,3,3,3,3}<br />[[Stericated 9-simplex]]
|| || || || || || || ||15120 ||1260
|- align=center
!13
|[[File:9-simplex t14.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}<br />t<sub>1,4</sub>{3,3,3,3,3,3,3,3}<br />[[Biruncinated 9-simplex]]
|| || || || || || || ||26460 ||2520
|- align=center
!14
|[[File:9-simplex t24.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}<br />t<sub>2,4</sub>{3,3,3,3,3,3,3,3}<br />[[Tricantellated 9-simplex]]
|| || || || || || || ||20160 ||2520
|- align=center
!15
|
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}<br />t<sub>3,4</sub>{3,3,3,3,3,3,3,3}<br />[[Quadritruncated 9-simplex]]
|| || || || || || || ||5670 ||1260
|- align=center
!16
|[[File:9-simplex t05.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,5</sub>{3,3,3,3,3,3,3,3}<br />[[Pentellated 9-simplex]]
|| || || || || || || ||15750 ||1260
|- align=center
!17
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}<br />t<sub>1,5</sub>{3,3,3,3,3,3,3,3}<br />[[Bistericated 9-simplex]]
|| || || || || || || ||37800 ||3150
|- align=center
!18
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node}}<br />t<sub>2,5</sub>{3,3,3,3,3,3,3,3}<br />[[Triruncinated 9-simplex]]
|| || || || || || || ||44100 ||4200
|- align=center BGCOLOR="#e0f0e0"
!19
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node}}<br />t<sub>3,5</sub>{3,3,3,3,3,3,3,3}<br />[[Quadricantellated 9-simplex]]
|| || || || || || || ||25200 ||3150
|- align=center
!20
|[[File:9-simplex t06.svg|60px]]
|
{{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexicated 9-simplex]]
|| || || || || || || ||10080 ||840
|- align=center
!21
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node}}<br />t<sub>1,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipentellated 9-simplex]]
|| || || || || || || ||31500 ||2520
|- align=center BGCOLOR="#e0f0e0"
!22
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node}}<br />t<sub>2,6</sub>{3,3,3,3,3,3,3,3}<br />[[Tristericated 9-simplex]]
|| || || || || || || ||50400 ||4200
|- align=center
!23
|[[File:9-simplex t07.svg|60px]]
|
{{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptellated 9-simplex]]
|| || || || || || || ||3780 ||360
|- align=center BGCOLOR="#e0f0e0"
!24
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}<br />t<sub>1,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexicated 9-simplex]]
|| || || || || || || ||15120 ||1260
|- align=center BGCOLOR="#e0f0e0"
!25
|[[File:9-simplex t08.svg|60px]]
|
{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octellated 9-simplex]]
|| || || || || || || ||720 ||90
|- align=center
!26
|[[File:9-simplex t012.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2</sub>{3,3,3,3,3,3,3,3}<br />[[Cantitruncated 9-simplex]]
|| || || || || || || ||3240 ||720
|- align=center
!27
|
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3</sub>{3,3,3,3,3,3,3,3}<br />[[Runcitruncated 9-simplex]]
|| || || || || || || ||18900 ||2520
|- align=center
!28
|
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3</sub>{3,3,3,3,3,3,3,3}<br />[[Runcicantellated 9-simplex]]
|| || || || || || || ||12600 ||2520
|- align=center
!29
|[[File:9-simplex t123.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3</sub>{3,3,3,3,3,3,3,3}<br />[[Bicantitruncated 9-simplex]]
|| || || || || || || ||11340 ||2520
|- align=center
!30
|
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,4</sub>{3,3,3,3,3,3,3,3}<br />[[Steritruncated 9-simplex]]
|| || || || || || || ||47880 ||5040
|- align=center
!31
|
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,4</sub>{3,3,3,3,3,3,3,3}<br />[[Stericantellated 9-simplex]]
|| || || || || || || ||60480 ||7560
|- align=center
!32
|
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,4</sub>{3,3,3,3,3,3,3,3}<br />[[Biruncitruncated 9-simplex]]
|| || || || || || || ||52920 ||7560
|- align=center
!33
|
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,4</sub>{3,3,3,3,3,3,3,3}<br />[[Steriruncinated 9-simplex]]
|| || || || || || || ||27720 ||5040
|- align=center
!34
|
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}<br />t<sub>1,3,4</sub>{3,3,3,3,3,3,3,3}<br />[[Biruncicantellated 9-simplex]]
|| || || || || || || ||41580 ||7560
|- align=center
!35
|[[File:9-simplex t234.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}<br />t<sub>2,3,4</sub>{3,3,3,3,3,3,3,3}<br />[[Tricantitruncated 9-simplex]]
|| || || || || || || ||22680 ||5040
|- align=center
!36
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,5</sub>{3,3,3,3,3,3,3,3}<br />[[Pentitruncated 9-simplex]]
|| || || || || || || ||66150 ||6300
|- align=center
!37
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,5</sub>{3,3,3,3,3,3,3,3}<br />[[Penticantellated 9-simplex]]
|| || || || || || || ||126000 ||12600
|- align=center
!38
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,5</sub>{3,3,3,3,3,3,3,3}<br />[[Bisteritruncated 9-simplex]]
|| || || || || || || ||107100 ||12600
|- align=center
!39
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,5</sub>{3,3,3,3,3,3,3,3}<br />[[Pentiruncinated 9-simplex]]
|| || || || || || || ||107100 ||12600
|- align=center
!40
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}<br />t<sub>1,3,5</sub>{3,3,3,3,3,3,3,3}<br />[[Bistericantellated 9-simplex]]
|| || || || || || || ||151200 ||18900
|- align=center
!41
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}<br />t<sub>2,3,5</sub>{3,3,3,3,3,3,3,3}<br />[[Triruncitruncated 9-simplex]]
|| || || || || || || ||81900 ||12600
|- align=center
!42
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Pentistericated 9-simplex]]
|| || || || || || || ||37800 ||6300
|- align=center
!43
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}<br />t<sub>1,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Bisteriruncinated 9-simplex]]
|| || || || || || || ||81900 ||12600
|- align=center
!44
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node}}<br />t<sub>2,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Triruncicantellated 9-simplex]]
|| || || || || || || ||75600 ||12600
|- align=center BGCOLOR="#e0f0e0"
!45
|[[File:9-simplex t345.svg|60px]]
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node}}<br />t<sub>3,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Quadricantitruncated 9-simplex]]
|| || || || || || || ||28350 ||6300
|- align=center
!46
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexitruncated 9-simplex]]
|| || || || || || || ||52920 ||5040
|- align=center
!47
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexicantellated 9-simplex]]
|| || || || || || || ||138600 ||12600
|- align=center
!48
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipentitruncated 9-simplex]]
|| || || || || || || ||113400 ||12600
|- align=center
!49
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexiruncinated 9-simplex]]
|| || || || || || || ||176400 ||16800
|- align=center
!50
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}<br />t<sub>1,3,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipenticantellated 9-simplex]]
|| || || || || || || ||239400 ||25200
|- align=center
!51
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node}}<br />t<sub>2,3,6</sub>{3,3,3,3,3,3,3,3}<br />[[Tristeritruncated 9-simplex]]
|| || || || || || || ||126000 ||16800
|- align=center
!52
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,4,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexistericated 9-simplex]]
|| || || || || || || ||113400 ||12600
|- align=center
!53
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}<br />t<sub>1,4,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipentiruncinated 9-simplex]]
|| || || || || || || ||226800 ||25200
|- align=center BGCOLOR="#e0f0e0"
!54
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node}}<br />t<sub>2,4,6</sub>{3,3,3,3,3,3,3,3}<br />[[Tristericantellated 9-simplex]]
|| || || || || || || ||201600 ||25200
|- align=center
!55
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipentellated 9-simplex]]
|| || || || || || || ||32760 ||5040
|- align=center
!56
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node}}<br />t<sub>1,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipentistericated 9-simplex]]
|| || || || || || || ||94500 ||12600
|- align=center
!57
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptitruncated 9-simplex]]
|| || || || || || || ||23940 ||2520
|- align=center
!58
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,7</sub>{3,3,3,3,3,3,3,3}<br />[[Hepticantellated 9-simplex]]
|| || || || || || || ||83160 ||7560
|- align=center
!59
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexitruncated 9-simplex]]
|| || || || || || || ||64260 ||7560
|- align=center
!60
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptiruncinated 9-simplex]]
|| || || || || || || ||144900 ||12600
|- align=center
!61
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node}}<br />t<sub>1,3,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexicantellated 9-simplex]]
|| || || || || || || ||189000 ||18900
|- align=center
!62
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,4,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptistericated 9-simplex]]
|| || || || || || || ||138600 ||12600
|- align=center BGCOLOR="#e0f0e0"
!63
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node}}<br />t<sub>1,4,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexiruncinated 9-simplex]]
|| || || || || || || ||264600 ||25200
|- align=center
!64
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipentellated 9-simplex]]
|| || || || || || || ||71820 ||7560
|- align=center
!65
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexicated 9-simplex]]
|| || || || || || || ||17640 ||2520
|- align=center
!66
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octitruncated 9-simplex]]
|| || || || || || || ||5400 ||720
|- align=center
!67
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octicantellated 9-simplex]]
|| || || || || || || ||25200 ||2520
|- align=center
!68
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiruncinated 9-simplex]]
|| || || || || || || ||57960 ||5040
|- align=center BGCOLOR="#e0f0e0"
!69
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,4,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octistericated 9-simplex]]
|| || || || || || || ||75600 ||6300
|- align=center
!70
|
|
{{CDD|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3</sub>{3,3,3,3,3,3,3,3}<br />[[Runcicantitruncated 9-simplex]]
|| || || || || || || ||22680 ||5040
|- align=center
!71
|
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4</sub>{3,3,3,3,3,3,3,3}<br />[[Stericantitruncated 9-simplex]]
|| || || || || || || ||105840 ||15120
|- align=center
!72
|
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,4</sub>{3,3,3,3,3,3,3,3}<br />[[Steriruncitruncated 9-simplex]]
|| || || || || || || ||75600 ||15120
|- align=center
!73
|
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,4</sub>{3,3,3,3,3,3,3,3}<br />[[Steriruncicantellated 9-simplex]]
|| || || || || || || ||75600 ||15120
|- align=center
!74
|
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,4</sub>{3,3,3,3,3,3,3,3}<br />[[Biruncicantitruncated 9-simplex]]
|| || || || || || || ||68040 ||15120
|- align=center
!75
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,5</sub>{3,3,3,3,3,3,3,3}<br />[[Penticantitruncated 9-simplex]]
|| || || || || || || ||214200 ||25200
|- align=center
!76
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,5</sub>{3,3,3,3,3,3,3,3}<br />[[Pentiruncitruncated 9-simplex]]
|| || || || || || || ||283500 ||37800
|- align=center
!77
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,5</sub>{3,3,3,3,3,3,3,3}<br />[[Pentiruncicantellated 9-simplex]]
|| || || || || || || ||264600 ||37800
|- align=center
!78
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,5</sub>{3,3,3,3,3,3,3,3}<br />[[Bistericantitruncated 9-simplex]]
|| || || || || || || ||245700 ||37800
|- align=center
!79
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Pentisteritruncated 9-simplex]]
|| || || || || || || ||138600 ||25200
|- align=center
!80
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Pentistericantellated 9-simplex]]
|| || || || || || || ||226800 ||37800
|- align=center
!81
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Bisteriruncitruncated 9-simplex]]
|| || || || || || || ||189000 ||37800
|- align=center
!82
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Pentisteriruncinated 9-simplex]]
|| || || || || || || ||138600 ||25200
|- align=center
!83
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}<br />t<sub>1,3,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Bisteriruncicantellated 9-simplex]]
|| || || || || || || ||207900 ||37800
|- align=center
!84
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}<br />t<sub>2,3,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Triruncicantitruncated 9-simplex]]
|| || || || || || || ||113400 ||25200
|- align=center
!85
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexicantitruncated 9-simplex]]
|| || || || || || || ||226800 ||25200
|- align=center
!86
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexiruncitruncated 9-simplex]]
|| || || || || || || ||453600 ||50400
|- align=center
!87
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexiruncicantellated 9-simplex]]
|| || || || || || || ||403200 ||50400
|- align=center
!88
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipenticantitruncated 9-simplex]]
|| || || || || || || ||378000 ||50400
|- align=center
!89
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,4,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexisteritruncated 9-simplex]]
|| || || || || || || ||403200 ||50400
|- align=center
!90
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,4,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexistericantellated 9-simplex]]
|| || || || || || || ||604800 ||75600
|- align=center
!91
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,4,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipentiruncitruncated 9-simplex]]
|| || || || || || || ||529200 ||75600
|- align=center
!92
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,4,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexisteriruncinated 9-simplex]]
|| || || || || || || ||352800 ||50400
|- align=center
!93
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}<br />t<sub>1,3,4,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipentiruncicantellated 9-simplex]]
|| || || || || || || ||529200 ||75600
|- align=center
!94
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node}}<br />t<sub>2,3,4,6</sub>{3,3,3,3,3,3,3,3}<br />[[Tristericantitruncated 9-simplex]]
|| || || || || || || ||302400 ||50400
|- align=center
!95
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipentitruncated 9-simplex]]
|| || || || || || || ||151200 ||25200
|- align=center
!96
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipenticantellated 9-simplex]]
|| || || || || || || ||352800 ||50400
|- align=center
!97
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipentisteritruncated 9-simplex]]
|| || || || || || || ||277200 ||50400
|- align=center
!98
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipentiruncinated 9-simplex]]
|| || || || || || || ||352800 ||50400
|- align=center
!99
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}<br />t<sub>1,3,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipentistericantellated 9-simplex]]
|| || || || || || || ||491400 ||75600
|- align=center BGCOLOR="#e0f0e0"
!100
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node}}<br />t<sub>2,3,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Tristeriruncitruncated 9-simplex]]
|| || || || || || || ||252000 ||50400
|- align=center
!101
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,4,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipentistericated 9-simplex]]
|| || || || || || || ||151200 ||25200
|- align=center
!102
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node}}<br />t<sub>1,4,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipentisteriruncinated 9-simplex]]
|| || || || || || || ||327600 ||50400
|- align=center
!103
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,7</sub>{3,3,3,3,3,3,3,3}<br />[[Hepticantitruncated 9-simplex]]
|| || || || || || || ||128520 ||15120
|- align=center
!104
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptiruncitruncated 9-simplex]]
|| || || || || || || ||359100 ||37800
|- align=center
!105
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptiruncicantellated 9-simplex]]
|| || || || || || || ||302400 ||37800
|- align=center
!106
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexicantitruncated 9-simplex]]
|| || || || || || || ||283500 ||37800
|- align=center
!107
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,4,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptisteritruncated 9-simplex]]
|| || || || || || || ||478800 ||50400
|- align=center
!108
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,4,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptistericantellated 9-simplex]]
|| || || || || || || ||680400 ||75600
|- align=center
!109
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,4,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexiruncitruncated 9-simplex]]
|| || || || || || || ||604800 ||75600
|- align=center
!110
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,4,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptisteriruncinated 9-simplex]]
|| || || || || || || ||378000 ||50400
|- align=center
!111
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node}}<br />t<sub>1,3,4,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexiruncicantellated 9-simplex]]
|| || || || || || || ||567000 ||75600
|- align=center
!112
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipentitruncated 9-simplex]]
|| || || || || || || ||321300 ||37800
|- align=center
!113
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipenticantellated 9-simplex]]
|| || || || || || || ||680400 ||75600
|- align=center
!114
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexisteritruncated 9-simplex]]
|| || || || || || || ||567000 ||75600
|- align=center
!115
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipentiruncinated 9-simplex]]
|| || || || || || || ||642600 ||75600
|- align=center BGCOLOR="#e0f0e0"
!116
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node}}<br />t<sub>1,3,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexistericantellated 9-simplex]]
|| || || || || || || ||907200 ||113400
|- align=center
!117
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,4,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipentistericated 9-simplex]]
|| || || || || || || ||264600 ||37800
|- align=center
!118
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexitruncated 9-simplex]]
|| || || || || || || ||98280 ||15120
|- align=center
!119
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexicantellated 9-simplex]]
|| || || || || || || ||302400 ||37800
|- align=center BGCOLOR="#e0f0e0"
!120
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexipentitruncated 9-simplex]]
|| || || || || || || ||226800 ||37800
|- align=center
!121
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexiruncinated 9-simplex]]
|| || || || || || || ||428400 ||50400
|- align=center
!122
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,4,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexistericated 9-simplex]]
|| || || || || || || ||302400 ||37800
|- align=center
!123
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipentellated 9-simplex]]
|| || || || || || || ||98280 ||15120
|- align=center
!124
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octicantitruncated 9-simplex]]
|| || || || || || || ||35280 ||5040
|- align=center
!125
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiruncitruncated 9-simplex]]
|| || || || || || || ||136080 ||15120
|- align=center
!126
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiruncicantellated 9-simplex]]
|| || || || || || || ||105840 ||15120
|- align=center
!127
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,4,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octisteritruncated 9-simplex]]
|| || || || || || || ||252000 ||25200
|- align=center
!128
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,4,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octistericantellated 9-simplex]]
|| || || || || || || ||340200 ||37800
|- align=center
!129
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,4,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octisteriruncinated 9-simplex]]
|| || || || || || || ||176400 ||25200
|- align=center
!130
|
|
{{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,5,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octipentitruncated 9-simplex]]
|| || || || || || || ||252000 ||25200
|- align=center
!131
|
|
{{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,5,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octipenticantellated 9-simplex]]
|| || || || || || || ||504000 ||50400
|- align=center BGCOLOR="#e0f0e0"
!132
|
|
{{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,5,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octipentiruncinated 9-simplex]]
|| || || || || || || ||453600 ||50400
|- align=center
!133
|
|
{{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexitruncated 9-simplex]]
|| || || || || || || ||136080 ||15120
|- align=center BGCOLOR="#e0f0e0"
!134
|
|
{{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexicantellated 9-simplex]]
|| || || || || || || ||378000 ||37800
|- align=center BGCOLOR="#e0f0e0"
!135
|
|
{{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptitruncated 9-simplex]]
|| || || || || || || ||35280 ||5040
|- align=center
!136
|
|
{{CDD|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4</sub>{3,3,3,3,3,3,3,3}<br />[[Steriruncicantitruncated 9-simplex]]
|| || || || || || || ||136080 ||30240
|- align=center
!137
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,5</sub>{3,3,3,3,3,3,3,3}<br />[[Pentiruncicantitruncated 9-simplex]]
|| || || || || || || ||491400 ||75600
|- align=center
!138
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Pentistericantitruncated 9-simplex]]
|| || || || || || || ||378000 ||75600
|- align=center
!139
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Pentisteriruncitruncated 9-simplex]]
|| || || || || || || ||378000 ||75600
|- align=center
!140
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Pentisteriruncicantellated 9-simplex]]
|| || || || || || || ||378000 ||75600
|- align=center
!141
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Bisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||340200 ||75600
|- align=center
!142
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexiruncicantitruncated 9-simplex]]
|| || || || || || || ||756000 ||100800
|- align=center
!143
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexistericantitruncated 9-simplex]]
|| || || || || || || ||1058400 ||151200
|- align=center
!144
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,4,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexisteriruncitruncated 9-simplex]]
|| || || || || || || ||982800 ||151200
|- align=center
!145
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,4,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexisteriruncicantellated 9-simplex]]
|| || || || || || || ||982800 ||151200
|- align=center
!146
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,4,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipentiruncicantitruncated 9-simplex]]
|| || || || || || || ||907200 ||151200
|- align=center
!147
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipenticantitruncated 9-simplex]]
|| || || || || || || ||554400 ||100800
|- align=center
!148
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipentiruncitruncated 9-simplex]]
|| || || || || || || ||907200 ||151200
|- align=center
!149
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipentiruncicantellated 9-simplex]]
|| || || || || || || ||831600 ||151200
|- align=center
!150
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipentistericantitruncated 9-simplex]]
|| || || || || || || ||756000 ||151200
|- align=center
!151
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,4,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipentisteritruncated 9-simplex]]
|| || || || || || || ||554400 ||100800
|- align=center
!152
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,4,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipentistericantellated 9-simplex]]
|| || || || || || || ||907200 ||151200
|- align=center
!153
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,4,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipentisteriruncitruncated 9-simplex]]
|| || || || || || || ||756000 ||151200
|- align=center
!154
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,4,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipentisteriruncinated 9-simplex]]
|| || || || || || || ||554400 ||100800
|- align=center
!155
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}<br />t<sub>1,3,4,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipentisteriruncicantellated 9-simplex]]
|| || || || || || || ||831600 ||151200
|- align=center BGCOLOR="#e0f0e0"
!156
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node}}<br />t<sub>2,3,4,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Tristeriruncicantitruncated 9-simplex]]
|| || || || || || || ||453600 ||100800
|- align=center
!157
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptiruncicantitruncated 9-simplex]]
|| || || || || || || ||567000 ||75600
|- align=center
!158
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptistericantitruncated 9-simplex]]
|| || || || || || || ||1209600 ||151200
|- align=center
!159
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,4,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptisteriruncitruncated 9-simplex]]
|| || || || || || || ||1058400 ||151200
|- align=center
!160
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,4,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptisteriruncicantellated 9-simplex]]
|| || || || || || || ||1058400 ||151200
|- align=center
!161
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,4,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexiruncicantitruncated 9-simplex]]
|| || || || || || || ||982800 ||151200
|- align=center
!162
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipenticantitruncated 9-simplex]]
|| || || || || || || ||1134000 ||151200
|- align=center
!163
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipentiruncitruncated 9-simplex]]
|| || || || || || || ||1701000 ||226800
|- align=center
!164
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipentiruncicantellated 9-simplex]]
|| || || || || || || ||1587600 ||226800
|- align=center
!165
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexistericantitruncated 9-simplex]]
|| || || || || || || ||1474200 ||226800
|- align=center
!166
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,4,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipentisteritruncated 9-simplex]]
|| || || || || || || ||982800 ||151200
|- align=center
!167
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,4,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipentistericantellated 9-simplex]]
|| || || || || || || ||1587600 ||226800
|- align=center
!168
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,4,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexisteriruncitruncated 9-simplex]]
|| || || || || || || ||1360800 ||226800
|- align=center
!169
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,4,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipentisteriruncinated 9-simplex]]
|| || || || || || || ||982800 ||151200
|- align=center BGCOLOR="#e0f0e0"
!170
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node}}<br />t<sub>1,3,4,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexisteriruncicantellated 9-simplex]]
|| || || || || || || ||1474200 ||226800
|- align=center
!171
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexicantitruncated 9-simplex]]
|| || || || || || || ||453600 ||75600
|- align=center
!172
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexiruncitruncated 9-simplex]]
|| || || || || || || ||1058400 ||151200
|- align=center
!173
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexiruncicantellated 9-simplex]]
|| || || || || || || ||907200 ||151200
|- align=center
!174
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexipenticantitruncated 9-simplex]]
|| || || || || || || ||831600 ||151200
|- align=center
!175
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,4,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexisteritruncated 9-simplex]]
|| || || || || || || ||1058400 ||151200
|- align=center
!176
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,4,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexistericantellated 9-simplex]]
|| || || || || || || ||1587600 ||226800
|- align=center BGCOLOR="#e0f0e0"
!177
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,4,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexipentiruncitruncated 9-simplex]]
|| || || || || || || ||1360800 ||226800
|- align=center
!178
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,4,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexisteriruncinated 9-simplex]]
|| || || || || || || ||907200 ||151200
|- align=center
!179
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipentitruncated 9-simplex]]
|| || || || || || || ||453600 ||75600
|- align=center
!180
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipenticantellated 9-simplex]]
|| || || || || || || ||1058400 ||151200
|- align=center
!181
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipentiruncinated 9-simplex]]
|| || || || || || || ||1058400 ||151200
|- align=center
!182
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1}}<br />t<sub>0,4,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipentistericated 9-simplex]]
|| || || || || || || ||453600 ||75600
|- align=center
!183
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiruncicantitruncated 9-simplex]]
|| || || || || || || ||196560 ||30240
|- align=center
!184
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octistericantitruncated 9-simplex]]
|| || || || || || || ||604800 ||75600
|- align=center
!185
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,4,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octisteriruncitruncated 9-simplex]]
|| || || || || || || ||491400 ||75600
|- align=center
!186
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,4,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octisteriruncicantellated 9-simplex]]
|| || || || || || || ||491400 ||75600
|- align=center
!187
|
|
{{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,5,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octipenticantitruncated 9-simplex]]
|| || || || || || || ||856800 ||100800
|- align=center
!188
|
|
{{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,5,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octipentiruncitruncated 9-simplex]]
|| || || || || || || ||1209600 ||151200
|- align=center
!189
|
|
{{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,5,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octipentiruncicantellated 9-simplex]]
|| || || || || || || ||1134000 ||151200
|- align=center
!190
|
|
{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,4,5,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octipentisteritruncated 9-simplex]]
|| || || || || || || ||655200 ||100800
|- align=center
!191
|
|
{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,4,5,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octipentistericantellated 9-simplex]]
|| || || || || || || ||1058400 ||151200
|- align=center BGCOLOR="#e0f0e0"
!192
|
|
{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,4,5,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octipentisteriruncinated 9-simplex]]
|| || || || || || || ||655200 ||100800
|- align=center
!193
|
|
{{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexicantitruncated 9-simplex]]
|| || || || || || || ||604800 ||75600
|- align=center
!194
|
|
{{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexiruncitruncated 9-simplex]]
|| || || || || || || ||1285200 ||151200
|- align=center
!195
|
|
{{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexiruncicantellated 9-simplex]]
|| || || || || || || ||1134000 ||151200
|- align=center
!196
|
|
{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,4,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexisteritruncated 9-simplex]]
|| || || || || || || ||1209600 ||151200
|- align=center BGCOLOR="#e0f0e0"
!197
|
|
{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,4,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexistericantellated 9-simplex]]
|| || || || || || || ||1814400 ||226800
|- align=center
!198
|
|
{{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,5,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexipentitruncated 9-simplex]]
|| || || || || || || ||491400 ||75600
|- align=center
!199
|
|
{{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihepticantitruncated 9-simplex]]
|| || || || || || || ||196560 ||30240
|- align=center
!200
|
|
{{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptiruncitruncated 9-simplex]]
|| || || || || || || ||604800 ||75600
|- align=center BGCOLOR="#e0f0e0"
!201
|
|
{{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,4,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptisteritruncated 9-simplex]]
|| || || || || || || ||856800 ||100800
|- align=center
!202
|
|
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,5</sub>{3,3,3,3,3,3,3,3}<br />[[Pentisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||680400 ||151200
|- align=center
!203
|
|
{{CDD|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||1814400 ||302400
|- align=center
!204
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipentiruncicantitruncated 9-simplex]]
|| || || || || || || ||1512000 ||302400
|- align=center
!205
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipentistericantitruncated 9-simplex]]
|| || || || || || || ||1512000 ||302400
|- align=center
!206
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,4,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipentisteriruncitruncated 9-simplex]]
|| || || || || || || ||1512000 ||302400
|- align=center
!207
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,4,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipentisteriruncicantellated 9-simplex]]
|| || || || || || || ||1512000 ||302400
|- align=center
!208
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,4,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Bipentisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||1360800 ||302400
|- align=center
!209
|
|
{{CDD|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||1965600 ||302400
|- align=center
!210
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipentiruncicantitruncated 9-simplex]]
|| || || || || || || ||2948400 ||453600
|- align=center
!211
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipentistericantitruncated 9-simplex]]
|| || || || || || || ||2721600 ||453600
|- align=center
!212
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,4,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipentisteriruncitruncated 9-simplex]]
|| || || || || || || ||2721600 ||453600
|- align=center
!213
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,4,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipentisteriruncicantellated 9-simplex]]
|| || || || || || || ||2721600 ||453600
|- align=center
!214
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,4,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||2494800 ||453600
|- align=center
!215
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexiruncicantitruncated 9-simplex]]
|| || || || || || || ||1663200 ||302400
|- align=center
!216
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexistericantitruncated 9-simplex]]
|| || || || || || || ||2721600 ||453600
|- align=center
!217
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,4,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexisteriruncitruncated 9-simplex]]
|| || || || || || || ||2494800 ||453600
|- align=center
!218
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,4,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexisteriruncicantellated 9-simplex]]
|| || || || || || || ||2494800 ||453600
|- align=center
!219
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,4,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexipentiruncicantitruncated 9-simplex]]
|| || || || || || || ||2268000 ||453600
|- align=center
!220
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipenticantitruncated 9-simplex]]
|| || || || || || || ||1663200 ||302400
|- align=center
!221
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipentiruncitruncated 9-simplex]]
|| || || || || || || ||2721600 ||453600
|- align=center
!222
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipentiruncicantellated 9-simplex]]
|| || || || || || || ||2494800 ||453600
|- align=center BGCOLOR="#e0f0e0"
!223
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexipentistericantitruncated 9-simplex]]
|| || || || || || || ||2268000 ||453600
|- align=center
!224
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,4,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipentisteritruncated 9-simplex]]
|| || || || || || || ||1663200 ||302400
|- align=center
!225
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,4,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipentistericantellated 9-simplex]]
|| || || || || || || ||2721600 ||453600
|- align=center
!226
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1}}<br />t<sub>0,3,4,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipentisteriruncinated 9-simplex]]
|| || || || || || || ||1663200 ||302400
|- align=center
!227
|
|
{{CDD|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||907200 ||151200
|- align=center
!228
|
|
{{CDD|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,5,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octipentiruncicantitruncated 9-simplex]]
|| || || || || || || ||2116800 ||302400
|- align=center
!229
|
|
{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4,5,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octipentistericantitruncated 9-simplex]]
|| || || || || || || ||1814400 ||302400
|- align=center
!230
|
|
{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,4,5,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octipentisteriruncitruncated 9-simplex]]
|| || || || || || || ||1814400 ||302400
|- align=center
!231
|
|
{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,4,5,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octipentisteriruncicantellated 9-simplex]]
|| || || || || || || ||1814400 ||302400
|- align=center
!232
|
|
{{CDD|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexiruncicantitruncated 9-simplex]]
|| || || || || || || ||2116800 ||302400
|- align=center
!233
|
|
{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexistericantitruncated 9-simplex]]
|| || || || || || || ||3175200 ||453600
|- align=center
!234
|
|
{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,4,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexisteriruncitruncated 9-simplex]]
|| || || || || || || ||2948400 ||453600
|- align=center
!235
|
|
{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,4,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexisteriruncicantellated 9-simplex]]
|| || || || || || || ||2948400 ||453600
|- align=center
!236
|
|
{{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,5,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexipenticantitruncated 9-simplex]]
|| || || || || || || ||1814400 ||302400
|- align=center
!237
|
|
{{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,5,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexipentiruncitruncated 9-simplex]]
|| || || || || || || ||2948400 ||453600
|- align=center BGCOLOR="#e0f0e0"
!238
|
|
{{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,5,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexipentiruncicantellated 9-simplex]]
|| || || || || || || ||2721600 ||453600
|- align=center
!239
|
|
{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,4,5,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexipentisteritruncated 9-simplex]]
|| || || || || || || ||1814400 ||302400
|- align=center
!240
|
|
{{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptiruncicantitruncated 9-simplex]]
|| || || || || || || ||907200 ||151200
|- align=center
!241
|
|
{{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptistericantitruncated 9-simplex]]
|| || || || || || || ||2116800 ||302400
|- align=center
!242
|
|
{{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,4,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptisteriruncitruncated 9-simplex]]
|| || || || || || || ||1814400 ||302400
|- align=center
!243
|
|
{{CDD|node_1|3|node_1|3|node|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,5,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptipenticantitruncated 9-simplex]]
|| || || || || || || ||2116800 ||302400
|- align=center BGCOLOR="#e0f0e0"
!244
|
|
{{CDD|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,5,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptipentiruncitruncated 9-simplex]]
|| || || || || || || ||3175200 ||453600
|- align=center BGCOLOR="#e0f0e0"
!245
|
|
{{CDD|node_1|3|node_1|3|node_1|3|node|3|node|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,6,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptihexicantitruncated 9-simplex]]
|| || || || || || || ||907200 ||151200
|- align=center
!246
|
|
{{CDD|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,5,6</sub>{3,3,3,3,3,3,3,3}<br />[[Hexipentisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||2721600 ||604800
|- align=center
!247
|
|
{{CDD|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,5,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptipentisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||4989600 ||907200
|- align=center
!248
|
|
{{CDD|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||4536000 ||907200
|- align=center
!249
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipentiruncicantitruncated 9-simplex]]
|| || || || || || || ||4536000 ||907200
|- align=center
!250
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipentistericantitruncated 9-simplex]]
|| || || || || || || ||4536000 ||907200
|- align=center
!251
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,4,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipentisteriruncitruncated 9-simplex]]
|| || || || || || || ||4536000 ||907200
|- align=center
!252
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,4,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipentisteriruncicantellated 9-simplex]]
|| || || || || || || ||4536000 ||907200
|- align=center BGCOLOR="#e0f0e0"
!253
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node}}<br />t<sub>1,2,3,4,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Bihexipentisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||4082400 ||907200
|- align=center
!254
|
|
{{CDD|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,5,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octipentisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||3326400 ||604800
|- align=center
!255
|
|
{{CDD|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||5443200 ||907200
|- align=center
!256
|
|
{{CDD|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,5,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexipentiruncicantitruncated 9-simplex]]
|| || || || || || || ||4989600 ||907200
|- align=center
!257
|
|
{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4,5,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexipentistericantitruncated 9-simplex]]
|| || || || || || || ||4989600 ||907200
|- align=center
!258
|
|
{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,4,5,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexipentisteriruncitruncated 9-simplex]]
|| || || || || || || ||4989600 ||907200
|- align=center BGCOLOR="#e0f0e0"
!259
|
|
{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1}}<br />t<sub>0,2,3,4,5,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexipentisteriruncicantellated 9-simplex]]
|| || || || || || || ||4989600 ||907200
|- align=center
!260
|
|
{{CDD|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||3326400 ||604800
|- align=center
!261
|
|
{{CDD|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,5,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptipentiruncicantitruncated 9-simplex]]
|| || || || || || || ||5443200 ||907200
|- align=center
!262
|
|
{{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4,5,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptipentistericantitruncated 9-simplex]]
|| || || || || || || ||4989600 ||907200
|- align=center BGCOLOR="#e0f0e0"
!263
|
|
{{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1}}<br />t<sub>0,1,3,4,5,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptipentisteriruncitruncated 9-simplex]]
|| || || || || || || ||4989600 ||907200
|- align=center
!264
|
|
{{CDD|node_1|3|node_1|3|node_1|3|node|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,6,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptihexiruncicantitruncated 9-simplex]]
|| || || || || || || ||3326400 ||604800
|- align=center BGCOLOR="#e0f0e0"
!265
|
|
{{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,4,6,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptihexistericantitruncated 9-simplex]]
|| || || || || || || ||5443200 ||907200
|- align=center
!266
|
|
{{CDD|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,5,6,7</sub>{3,3,3,3,3,3,3,3}<br />[[Heptihexipentisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||8164800 ||1814400
|- align=center
!267
|
|
{{CDD|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,5,6,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octihexipentisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||9072000 ||1814400
|- align=center
!268
|
|
{{CDD|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,5,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptipentisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||9072000 ||1814400
|- align=center
!269
|
|
{{CDD|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,6,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptihexisteriruncicantitruncated 9-simplex]]
|| || || || || || || ||9072000 ||1814400
|- align=center BGCOLOR="#e0f0e0"
!270
|
|
{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,5,6,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Octiheptihexipentiruncicantitruncated 9-simplex]]
|| || || || || || || ||9072000 ||1814400
|- align=center BGCOLOR="#e0f0e0"
!271
|
|
{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1|3|node_1}}<br />t<sub>0,1,2,3,4,5,6,7,8</sub>{3,3,3,3,3,3,3,3}<br />[[Omnitruncated 9-simplex]]
|| || || || || || || ||16329600 ||3628800
|}
 
== The B<sub>9</sub> family ==
 
There are 511 forms based on all permutations of the [[Coxeter-Dynkin diagram]]s with one or more rings.
 
Eleven cases are shown below: Nine [[Rectification (geometry)|rectified]] forms and 2 truncations. Bowers-style acronym names are given in parentheses for cross-referencing. Bowers-style acronym names are given in parentheses for cross-referencing.
 
{| class="wikitable"
!rowspan=2|#
!rowspan=2|Graph
!rowspan=2|[[Coxeter-Dynkin diagram]]<br />[[Schläfli symbol]]<br />Name
!colspan=10|Element counts
|-
! 8-faces
! 7-faces
! 6-faces
! 5-faces
! 4-faces
! Cells
! Faces
! Edges
! Vertices
|- align=center
!1
|[[File:9-cube.svg|60px]]
| {{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}<br />t<sub>0</sub>{4,3,3,3,3,3,3,3}<br />[[9-cube]] (enne)
|18||144||672||2016||4032||5376||4608||2304||512
|- align=center
!2
|[[File:Truncated 9-cube.png|60px]]
| {{CDD|node_1|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}<br />t<sub>0,1</sub>{4,3,3,3,3,3,3,3}<br />[[Truncated 9-cube]] (ten)
|| || || || || || || ||2304 ||4608
|- align=center
!3
|[[File:Rectified 9-cube.png|60px]]
| {{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node}}<br />t<sub>1</sub>{4,3,3,3,3,3,3,3}<br />[[Rectified 9-cube]] (ren)
|| || || || || || || ||18432 ||2304
|- align=center
!4
|[[File:Birectified 9-cube.png|60px]]
| {{CDD|node|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node}}<br />t<sub>2</sub>{4,3,3,3,3,3,3,3}<br />[[Birectified 9-cube]] (barn)
|| || || || || || || ||64512 ||4608
|- align=center
!5
|[[File:Quintirectified 9-orthoplex.png|60px]]
| {{CDD|node|4|node|3|node|3|node_1|3|node|3|node|3|node|3|node|3|node}}<br />t<sub>3</sub>{4,3,3,3,3,3,3,3}<br />[[Trirectified 9-cube]] (tarn)
|| || || || || || || ||96768 ||5376
|- align=center
!6
|[[File:Quadrirectified 9-orthoplex.png|60px]]
| {{CDD|node|4|node|3|node|3|node|3|node_1|3|node|3|node|3|node|3|node}}<br />t<sub>4</sub>{4,3,3,3,3,3,3,3}<br />[[Quadrirectified 9-cube]] (nav)<br />(Quadrirectified 9-orthoplex)
|| || || || || || || || 80640|| 4032
|- align=center
!7
|[[File:Trirectified 9-orthoplex.png|60px]]
| {{CDD|node|4|node|3|node|3|node|3|node|3|node_1|3|node|3|node|3|node}}<br />t<sub>3</sub>{3,3,3,3,3,3,3,4}<br />[[Trirectified 9-orthoplex]] (tarv)
|| || || || || || || ||40320 ||2016
|- align=center
!8
|[[File:Birectified 9-orthoplex.png|60px]]
| {{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node|3|node}}<br />t<sub>2</sub>{3,3,3,3,3,3,3,4}<br />[[Birectified 9-orthoplex]] (brav)
|| || || || || || || ||12096 ||672
|- align=center
!9
|[[File:Rectified heptacross.png|60px]]
| {{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}<br />t<sub>1</sub>{3,3,3,3,3,3,3,4}<br />[[Rectified 9-orthoplex]] (riv)
| ||  || || || || || ||2016 ||144
|- align=center
!10
|[[File:Truncated 9-orthoplex.png|60px]]
| {{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}}<br />t<sub>0,1</sub>{3,3,3,3,3,3,3,4}<br />[[Truncated 9-orthoplex]] (tiv)
| || || || || || || ||2160 || 288
|- align=center
!11
|[[File:Cross graph 9.png|60px]]
| {{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}<br />t<sub>0</sub>{3,3,3,3,3,3,3,4}<br />[[9-orthoplex]] (vee)
|512||2304||4608||5376||4032||2016||672||144||18
|}
 
== The D<sub>9</sub> family ==
 
The D<sub>9</sub> family has symmetry of order 92,897,280 (9 [[factorial]] × 2<sup>8</sup>).
 
This family has 3×128−1=383 Wythoffian uniform polytopes, generated by marking one or more nodes of the D<sub>9</sub> [[Coxeter-Dynkin diagram]]. Of these, 255 (2×128−1) are repeated from the B<sub>9</sub> family and 128 are unique to this family, with the eight 1 or 2 ringed forms listed below. Bowers-style acronym names are given in parentheses for cross-referencing.
 
{| class="wikitable"
!rowspan=2|#
!colspan=11|[[Coxeter plane]] graphs
!rowspan=2|[[Coxeter-Dynkin diagram]]<BR>[[Schläfli symbol]]
!rowspan=2|Base point<BR>(Alternately signed)
!colspan=9|Element counts
!rowspan=2|Circumrad
|-
! B<sub>9</sub>||D<sub>9</sub>|| D<sub>8</sub>|| D<sub>7</sub>|| D<sub>6</sub>|| D<sub>5</sub>|| D<sub>4</sub>|| D<sub>3</sub>|| A<sub>7</sub>|| A<sub>5</sub>|| A<sub>3</sub>|| 8|| 7|| 6|| 5|| 4|| 3|| 2|| 1|| 0
|- align=center
!1
||[[File:9-demicube t0 B9.svg|60px]]||[[File:9-demicube t0 D9.svg|60px]]||[[File:9-demicube t0 D8.svg|60px]]||[[File:9-demicube t0 D7.svg|60px]]||[[File:9-demicube t0 D6.svg|60px]]||[[File:9-demicube t0 D5.svg|60px]]||[[File:9-demicube t0 D4.svg|60px]]||[[File:9-demicube t0 D3.svg|60px]]||[[File:9-demicube t0 A7.svg|60px]]||[[File:9-demicube t0 A5.svg|60px]]||[[File:9-demicube t0 A3.svg|60px]]||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node|3|node|3|node}}<BR>[[9-demicube]] (henne)||(1,1,1,1,1,1,1,1,1)||274||2448||9888||23520||36288||37632||21404||4608||256||1.0606601
|- align=center
!2
||[[File:9-demicube t01 B9.svg|60px]]||[[File:9-demicube t01 D9.svg|60px]]||[[File:9-demicube t01 D8.svg|60px]]||[[File:9-demicube t01 D7.svg|60px]]||[[File:9-demicube t01 D6.svg|60px]]||[[File:9-demicube t01 D5.svg|60px]]||[[File:9-demicube t01 D4.svg|60px]]||[[File:9-demicube t01 D3.svg|60px]]||[[File:9-demicube t01 A7.svg|60px]]||[[File:9-demicube t01 A5.svg|60px]]||[[File:9-demicube t01 A3.svg|60px]]||{{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node|3|node|3|node}}<BR>[[Truncated 9-demicube]] (thenne)||(1,1,3,3,3,3,3,3,3)|| || || || || || || ||69120 ||9216||2.8504384
|- align=center
!3
||[[File:9-demicube t02 B9.svg|60px]]||[[File:9-demicube t02 D9.svg|60px]]||[[File:9-demicube t02 D8.svg|60px]]||[[File:9-demicube t02 D7.svg|60px]]||[[File:9-demicube t02 D6.svg|60px]]||[[File:9-demicube t02 D5.svg|60px]]||[[File:9-demicube t02 D4.svg|60px]]||[[File:9-demicube t02 D3.svg|60px]]||[[File:9-demicube t02 A7.svg|60px]]||[[File:9-demicube t02 A5.svg|60px]]||[[File:9-demicube t02 A3.svg|60px]]||{{CDD|nodes_10ru|split2|node|3|node_1|3|node|3|node|3|node|3|node|3|node}}<BR>[[Cantellated 9-demicube]]||(1,1,1,3,3,3,3,3,3)|| || || || || || || ||225792 ||21504||2.6692696
|- align=center
!4
||[[File:9-demicube t03 B9.svg|60px]]||[[File:9-demicube t03 D9.svg|60px]]||[[File:9-demicube t03 D8.svg|60px]]||[[File:9-demicube t03 D7.svg|60px]]||[[File:9-demicube t03 D6.svg|60px]]||[[File:9-demicube t03 D5.svg|60px]]||[[File:9-demicube t03 D4.svg|60px]]||[[File:9-demicube t03 D3.svg|60px]]||[[File:9-demicube t03 A7.svg|60px]]||[[File:9-demicube t03 A5.svg|60px]]||[[File:9-demicube t03 A3.svg|60px]]||{{CDD|nodes_10ru|split2|node|3|node|3|node_1|3|node|3|node|3|node|3|node}}<BR>[[Runcinated 9-demicube]]||(1,1,1,1,3,3,3,3,3)|| || || || || || || ||419328 ||32256||2.4748735
|- align=center
!5
||[[File:9-demicube t04 B9.svg|60px]]||[[File:9-demicube t04 D9.svg|60px]]||[[File:9-demicube t04 D8.svg|60px]]||[[File:9-demicube t04 D7.svg|60px]]||[[File:9-demicube t04 D6.svg|60px]]||[[File:9-demicube t04 D5.svg|60px]]||[[File:9-demicube t04 D4.svg|60px]]||[[File:9-demicube t04 D3.svg|60px]]||[[File:9-demicube t04 A7.svg|60px]]||[[File:9-demicube t04 A5.svg|60px]]||[[File:9-demicube t04 A3.svg|60px]]||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node_1|3|node|3|node|3|node}}<BR>[[Stericated 9-demicube]]||(1,1,1,1,1,3,3,3,3)|| || || || || || || ||483840 ||32256||2.2638462
|- align=center
!6
||[[File:9-demicube t05 B9.svg|60px]]||[[File:9-demicube t05 D9.svg|60px]]||[[File:9-demicube t05 D8.svg|60px]]||[[File:9-demicube t05 D7.svg|60px]]||[[File:9-demicube t05 D6.svg|60px]]||[[File:9-demicube t05 D5.svg|60px]]||[[File:9-demicube t05 D4.svg|60px]]||[[File:9-demicube t05 D3.svg|60px]]||[[File:9-demicube t05 A7.svg|60px]]||[[File:9-demicube t05 A5.svg|60px]]||[[File:9-demicube t05 A3.svg|60px]]||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node_1|3|node|3|node}}<BR>[[Pentellated 9-demicube]]||(1,1,1,1,1,1,3,3,3)|| || || || || || || ||354816 ||21504||2.0310094
|- align=center
!7
||[[File:9-demicube t06 B9.svg|60px]]||[[File:9-demicube t06 D9.svg|60px]]||[[File:9-demicube t06 D8.svg|60px]]||[[File:9-demicube t06 D7.svg|60px]]||[[File:9-demicube t06 D6.svg|60px]]||[[File:9-demicube t06 D5.svg|60px]]||[[File:9-demicube t06 D4.svg|60px]]||[[File:9-demicube t06 D3.svg|60px]]||[[File:9-demicube t06 A7.svg|60px]]||[[File:9-demicube t06 A5.svg|60px]]||[[File:9-demicube t06 A3.svg|60px]]||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node|3|node_1|3|node}}<BR>[[Hexicated 9-demicube]]||(1,1,1,1,1,1,1,3,3)|| || || || || || || ||161280 ||9216||1.7677668
|- align=center
!8
||[[File:9-demicube t07 B9.svg|60px]]||[[File:9-demicube t07 D9.svg|60px]]||[[File:9-demicube t07 D8.svg|60px]]||[[File:9-demicube t07 D7.svg|60px]]||[[File:9-demicube t07 D6.svg|60px]]||[[File:9-demicube t07 D5.svg|60px]]||[[File:9-demicube t07 D4.svg|60px]]||[[File:9-demicube t07 D3.svg|60px]]||[[File:9-demicube t07 A7.svg|60px]]||[[File:9-demicube t07 A5.svg|60px]]||[[File:9-demicube t07 A3.svg|60px]]||{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node|3|node|3|node_1}}<BR>[[Heptellated 9-demicube]]||(1,1,1,1,1,1,1,1,3)|| || || || || || || ||41472 ||2304||1.4577379
|}
 
== Regular and uniform honeycombs ==
[[File:Coxeter diagram affine rank9 correspondence.png|640px|thumb|Coxeter-Dynkin diagram correspondences between families and higher symmetry within diagrams. Nodes of the same color in each row represent identical mirrors. Black nodes are not active in the correspondence.]]
There are five fundamental affine [[Coxeter groups]] that generate regular and uniform tessellations in 8-space:
{| class=wikitable
!#
!colspan=2|[[Coxeter group]]
![[Coxeter diagram]]
!Forms
|- align=center
|1||<math>{\tilde{A}}_8</math>||[3<sup>[9]</sup>]||{{CDD|node|split1|nodes|3ab|nodes|3ab|nodes|3ab|branch}}||45
|- align=center
|2||<math>{\tilde{C}}_8</math>||[4,3<sup>6</sup>,4]||{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node|4|node}}||271
|- align=center
|3||<math>{\tilde{B}}_8</math>||h[4,3<sup>6</sup>,4]<br />[4,3<sup>5</sup>,3<sup>1,1</sup>]||{{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|3|node|4|node}}||383 (128 new)
|- align=center
|4||<math>{\tilde{D}}_8</math>||q[4,3<sup>6</sup>,4]<br />[3<sup>1,1</sup>,3<sup>4</sup>,3<sup>1,1</sup>]||{{CDD|nodes|split2|node|3|node|3|node|3|node|3|node|split1|nodes}}||155 (15 new)
|- align=center
|5||<math>{\tilde{E}}_8</math>||[3<sup>5,2,1</sup>]||{{CDD|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}||511
|}
 
Regular and uniform tessellations include:
* <math>{\tilde{A}}_8</math> 45 uniquely ringed forms
**[[8-simplex honeycomb]]: {3<sup>[9]</sup>} {{CDD|node_1|split1|nodes|3ab|nodes|3ab|nodes|3ab|branch}}
* <math>{\tilde{C}}_8</math> 271 uniquely ringed forms
** [[List of regular polytopes#Higher dimensions 3|Regular]] [[8-cube honeycomb]]: {4,3<sup>6</sup>,4}, {{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node|4|node}}
* <math>{\tilde{B}}_8</math>: 383 uniquely ringed forms, 255 shared with <math>{\tilde{C}}_8</math>, 128 new
** [[8-demicube honeycomb]]: h{4,3<sup>6</sup>,4} or {3<sup>1,1</sup>,3<sup>5</sup>,4}, {{CDD|node_h|4|node|3|node|3|node|3|node|3|node|3|node|3|node|4|node}} or {{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node|3|node|4|node}}
* <math>{\tilde{D}}_8</math>, [3<sup>1,1</sup>,3<sup>4</sup>,3<sup>1,1</sup>]: 155 unique ring permutations, and 15 are new, the first, {{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|split1|nodes_10lu}}, Coxeter called a [[quarter 8-cubic honeycomb]], representing as q{4,3<sup>6</sup>,4}, or q&delta;<sub>9</sub>.
* <math>{\tilde{E}}_8</math> 511 forms
** [[5 21 honeycomb|5<sub>21</sub> honeycomb]]:{{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea_1}}
** [[2 51 honeycomb|2<sub>51</sub> honeycomb]]: {{CDD|nodea_1|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
** [[1 52 honeycomb|1<sub>52</sub> honeycomb]]: {{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}
 
=== Regular and uniform hyperbolic honeycombs ===
 
There are no compact hyperbolic Coxeter groups of rank 9, groups that can generate honeycombs with all finite facets, and a finite [[vertex figure]]. However there are [[Coxeter-Dynkin_diagram#Rank_4_to_10|4 noncompact hyperbolic Coxeter groups]] of rank 9, each generating uniform honeycombs in 8-space as permutations of rings of the Coxeter diagrams.
 
{| class=wikitable
|align=right|<math>{\bar{P}}_8</math> = [3,3<sup>[8]</sup>]:<BR>{{CDD|node|split1|nodes|3ab|nodes|3ab|nodes|split2|node|3|node}}
|align=right|<math>{\bar{Q}}_8</math> = [3<sup>1,1</sup>,3<sup>3</sup>,3<sup>2,1</sup>]:<BR>{{CDD|nodea|3a|branch|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}}
|align=right|<math>{\bar{S}}_8</math> = [4,3<sup>4</sup>,3<sup>2,1</sup>]:<BR>{{CDD|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea|3a|nodea|4a|nodea}}
|align=right|<math>{\bar{T}}_8</math> = [3<sup>4,3,1</sup>]:<BR>{{CDD|nodea|3a|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea|3a|nodea}}
|}
 
== References ==
* [[Thorold Gosset|T. Gosset]]: ''On the Regular and Semi-Regular Figures in Space of n Dimensions'', [[Messenger of Mathematics]], Macmillan, 1900
* [[Alicia Boole Stott|A. Boole Stott]]: ''Geometrical deduction of semiregular from regular polytopes and space fillings'', Verhandelingen of the Koninklijke academy van Wetenschappen width unit Amsterdam, Eerste Sectie 11,1, Amsterdam, 1910
* [[Harold Scott MacDonald Coxeter|H.S.M. Coxeter]]:
** H.S.M. Coxeter, M.S. Longuet-Higgins und J.C.P. Miller: ''Uniform Polyhedra'', Philosophical Transactions of the Royal Society of London, Londne, 1954
** H.S.M. Coxeter, ''Regular Polytopes'', 3rd Edition, Dover New York, 1973
* '''Kaleidoscopes: Selected Writings of H.S.M. Coxeter''', editied by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html]
** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'', [Math. Zeit. 46 (1940) 380-407, MR 2,10]
** (Paper 23) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes II'', [Math. Zeit. 188 (1985) 559-591]
** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]
* [[Norman Johnson (mathematician)|N.W. Johnson]]: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D. Dissertation, University of Toronto, 1966
* {{KlitzingPolytopes|polyyotta.htm|9D|uniform polytopes (polyyotta)}}
 
== External links ==
* [http://www.steelpillow.com/polyhedra/ditela.html Polytope names]
* [http://www.polytope.net/hedrondude/topes.htm Polytopes of Various Dimensions], Jonathan Bowers
* [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]
* {{PolyCell | urlname = glossary.html| title = Glossary for hyperspace}}
{{Polytopes}}
{{Honeycombs}}
 
[[Category:9-polytopes]]

Latest revision as of 12:00, 11 December 2013

Graphs of three regular and related uniform polytopes

9-simplex
Rectified 9-simplex

Truncated 9-simplex
Cantellated 9-simplex

Runcinated 9-simplex
Stericated 9-simplex

Pentellated 9-simplex
Hexicated 9-simplex

Heptellated 9-simplex
Octellated 9-simplex

9-orthoplex
9-cube

Truncated 9-orthoplex
Truncated 9-cube

Rectified 9-orthoplex
Rectified 9-cube

9-demicube
Truncated 9-demicube

In nine-dimensional geometry, a polyyotton (or 9-polytope) is a polytope contained by 8-polytope facets. Each 7-polytope ridge being shared by exactly two 8-polytope facets.

A uniform polyyotton is one which is vertex-transitive, and constructed from uniform facets.

A proposed name for 9-polytope is polyyotton (plural: polyyotta), created from poly-, yotta- (a variation on octa, meaning eight) and -on.

Regular 9-polytopes

Regular 9-polytopes can be represented by the Schläfli symbol {p,q,r,s,t,u,v,w}, with w {p,q,r,s,t,u,v} 8-polytope facets around each peak.

There are exactly three such convex regular 9-polytopes:

  1. {3,3,3,3,3,3,3,3} - 9-simplex
  2. {4,3,3,3,3,3,3,3} - 9-cube
  3. {3,3,3,3,3,3,3,4} - 9-orthoplex

There are no nonconvex regular 9-polytopes.

Euler characteristic

The Euler characteristic for 9-polytopes that are topological 8-spheres (including all convex 9-polytopes) is zero. χ=V-E+F-C+f4-f5+f6-f7+f8=2.

Uniform 9-polytopes by fundamental Coxeter groups

Uniform 9-polytopes with reflective symmetry can be generated by these three Coxeter groups, represented by permutations of rings of the Coxeter-Dynkin diagrams:

Coxeter group Coxeter-Dynkin diagram
A9 [38] Template:CDD
B9 [4,37] Template:CDD
D9 [36,1,1] Template:CDD

Selected regular and uniform 9-polytopes from each family include:

The A9 family

The A9 family has symmetry of order 3628800 (10 factorial).

There are 256+16-1=271 forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings. These are all enumerated below. Bowers-style acronym names are given in parentheses for cross-referencing.

# Graph Coxeter-Dynkin diagram
Schläfli symbol
Name 		Element counts
8-faces 7-faces 6-faces 5-faces 4-faces Cells Faces Edges Vertices
1

Template:CDD
t0{3,3,3,3,3,3,3,3}
9-simplex (day)

10 45 120 210 252 210 120 45 10
2

Template:CDD
t1{3,3,3,3,3,3,3,3}
Rectified 9-simplex (reday)

360 45
3

Template:CDD
t2{3,3,3,3,3,3,3,3}
Birectified 9-simplex (breday)

1260 120
4

Template:CDD
t3{3,3,3,3,3,3,3,3}
Trirectified 9-simplex (treday)

2520 210
5

Template:CDD
t4{3,3,3,3,3,3,3,3}
Quadrirectified 9-simplex (icoy)

3150 252
6

Template:CDD
t0,1{3,3,3,3,3,3,3,3}
Truncated 9-simplex (teday)

405 90
7

Template:CDD
t0,2{3,3,3,3,3,3,3,3}
Cantellated 9-simplex

2880 360
8

Template:CDD
t1,2{3,3,3,3,3,3,3,3}
Bitruncated 9-simplex

1620 360
9

Template:CDD
t0,3{3,3,3,3,3,3,3,3}
Runcinated 9-simplex

8820 840
10

Template:CDD
t1,3{3,3,3,3,3,3,3,3}
Bicantellated 9-simplex

10080 1260
11

Template:CDD
t2,3{3,3,3,3,3,3,3,3}
Tritruncated 9-simplex (treday)

3780 840
12

Template:CDD
t0,4{3,3,3,3,3,3,3,3}
Stericated 9-simplex

15120 1260
13

Template:CDD
t1,4{3,3,3,3,3,3,3,3}
Biruncinated 9-simplex

26460 2520
14

Template:CDD
t2,4{3,3,3,3,3,3,3,3}
Tricantellated 9-simplex

20160 2520
15

Template:CDD
t3,4{3,3,3,3,3,3,3,3}
Quadritruncated 9-simplex

5670 1260
16

Template:CDD
t0,5{3,3,3,3,3,3,3,3}
Pentellated 9-simplex

15750 1260
17

Template:CDD
t1,5{3,3,3,3,3,3,3,3}
Bistericated 9-simplex

37800 3150
18

Template:CDD
t2,5{3,3,3,3,3,3,3,3}
Triruncinated 9-simplex

44100 4200
19

Template:CDD
t3,5{3,3,3,3,3,3,3,3}
Quadricantellated 9-simplex

25200 3150
20

Template:CDD
t0,6{3,3,3,3,3,3,3,3}
Hexicated 9-simplex

10080 840
21

Template:CDD
t1,6{3,3,3,3,3,3,3,3}
Bipentellated 9-simplex

31500 2520
22

Template:CDD
t2,6{3,3,3,3,3,3,3,3}
Tristericated 9-simplex

50400 4200
23

Template:CDD
t0,7{3,3,3,3,3,3,3,3}
Heptellated 9-simplex

3780 360
24

Template:CDD
t1,7{3,3,3,3,3,3,3,3}
Bihexicated 9-simplex

15120 1260
25

Template:CDD
t0,8{3,3,3,3,3,3,3,3}
Octellated 9-simplex

720 90
26

Template:CDD
t0,1,2{3,3,3,3,3,3,3,3}
Cantitruncated 9-simplex

3240 720
27

Template:CDD
t0,1,3{3,3,3,3,3,3,3,3}
Runcitruncated 9-simplex

18900 2520
28

Template:CDD
t0,2,3{3,3,3,3,3,3,3,3}
Runcicantellated 9-simplex

12600 2520
29

Template:CDD
t1,2,3{3,3,3,3,3,3,3,3}
Bicantitruncated 9-simplex

11340 2520
30

Template:CDD
t0,1,4{3,3,3,3,3,3,3,3}
Steritruncated 9-simplex

47880 5040
31

Template:CDD
t0,2,4{3,3,3,3,3,3,3,3}
Stericantellated 9-simplex

60480 7560
32

Template:CDD
t1,2,4{3,3,3,3,3,3,3,3}
Biruncitruncated 9-simplex

52920 7560
33

Template:CDD
t0,3,4{3,3,3,3,3,3,3,3}
Steriruncinated 9-simplex

27720 5040
34

Template:CDD
t1,3,4{3,3,3,3,3,3,3,3}
Biruncicantellated 9-simplex

41580 7560
35

Template:CDD
t2,3,4{3,3,3,3,3,3,3,3}
Tricantitruncated 9-simplex

22680 5040
36

Template:CDD
t0,1,5{3,3,3,3,3,3,3,3}
Pentitruncated 9-simplex

66150 6300
37

Template:CDD
t0,2,5{3,3,3,3,3,3,3,3}
Penticantellated 9-simplex

126000 12600
38

Template:CDD
t1,2,5{3,3,3,3,3,3,3,3}
Bisteritruncated 9-simplex

107100 12600
39

Template:CDD
t0,3,5{3,3,3,3,3,3,3,3}
Pentiruncinated 9-simplex

107100 12600
40

Template:CDD
t1,3,5{3,3,3,3,3,3,3,3}
Bistericantellated 9-simplex

151200 18900
41

Template:CDD
t2,3,5{3,3,3,3,3,3,3,3}
Triruncitruncated 9-simplex

81900 12600
42

Template:CDD
t0,4,5{3,3,3,3,3,3,3,3}
Pentistericated 9-simplex

37800 6300
43

Template:CDD
t1,4,5{3,3,3,3,3,3,3,3}
Bisteriruncinated 9-simplex

81900 12600
44

Template:CDD
t2,4,5{3,3,3,3,3,3,3,3}
Triruncicantellated 9-simplex

75600 12600
45

Template:CDD
t3,4,5{3,3,3,3,3,3,3,3}
Quadricantitruncated 9-simplex

28350 6300
46

Template:CDD
t0,1,6{3,3,3,3,3,3,3,3}
Hexitruncated 9-simplex

52920 5040
47

Template:CDD
t0,2,6{3,3,3,3,3,3,3,3}
Hexicantellated 9-simplex

138600 12600
48

Template:CDD
t1,2,6{3,3,3,3,3,3,3,3}
Bipentitruncated 9-simplex

113400 12600
49

Template:CDD
t0,3,6{3,3,3,3,3,3,3,3}
Hexiruncinated 9-simplex

176400 16800
50

Template:CDD
t1,3,6{3,3,3,3,3,3,3,3}
Bipenticantellated 9-simplex

239400 25200
51

Template:CDD
t2,3,6{3,3,3,3,3,3,3,3}
Tristeritruncated 9-simplex

126000 16800
52

Template:CDD
t0,4,6{3,3,3,3,3,3,3,3}
Hexistericated 9-simplex

113400 12600
53

Template:CDD
t1,4,6{3,3,3,3,3,3,3,3}
Bipentiruncinated 9-simplex

226800 25200
54

Template:CDD
t2,4,6{3,3,3,3,3,3,3,3}
Tristericantellated 9-simplex

201600 25200
55

Template:CDD
t0,5,6{3,3,3,3,3,3,3,3}
Hexipentellated 9-simplex

32760 5040
56

Template:CDD
t1,5,6{3,3,3,3,3,3,3,3}
Bipentistericated 9-simplex

94500 12600
57

Template:CDD
t0,1,7{3,3,3,3,3,3,3,3}
Heptitruncated 9-simplex

23940 2520
58

Template:CDD
t0,2,7{3,3,3,3,3,3,3,3}
Hepticantellated 9-simplex

83160 7560
59

Template:CDD
t1,2,7{3,3,3,3,3,3,3,3}
Bihexitruncated 9-simplex

64260 7560
60

Template:CDD
t0,3,7{3,3,3,3,3,3,3,3}
Heptiruncinated 9-simplex

144900 12600
61

Template:CDD
t1,3,7{3,3,3,3,3,3,3,3}
Bihexicantellated 9-simplex

189000 18900
62

Template:CDD
t0,4,7{3,3,3,3,3,3,3,3}
Heptistericated 9-simplex

138600 12600
63

Template:CDD
t1,4,7{3,3,3,3,3,3,3,3}
Bihexiruncinated 9-simplex

264600 25200
64

Template:CDD
t0,5,7{3,3,3,3,3,3,3,3}
Heptipentellated 9-simplex

71820 7560
65

Template:CDD
t0,6,7{3,3,3,3,3,3,3,3}
Heptihexicated 9-simplex

17640 2520
66

Template:CDD
t0,1,8{3,3,3,3,3,3,3,3}
Octitruncated 9-simplex

5400 720
67

Template:CDD
t0,2,8{3,3,3,3,3,3,3,3}
Octicantellated 9-simplex

25200 2520
68

Template:CDD
t0,3,8{3,3,3,3,3,3,3,3}
Octiruncinated 9-simplex

57960 5040
69

Template:CDD
t0,4,8{3,3,3,3,3,3,3,3}
Octistericated 9-simplex

75600 6300
70

Template:CDD
t0,1,2,3{3,3,3,3,3,3,3,3}
Runcicantitruncated 9-simplex

22680 5040
71

Template:CDD
t0,1,2,4{3,3,3,3,3,3,3,3}
Stericantitruncated 9-simplex

105840 15120
72

Template:CDD
t0,1,3,4{3,3,3,3,3,3,3,3}
Steriruncitruncated 9-simplex

75600 15120
73

Template:CDD
t0,2,3,4{3,3,3,3,3,3,3,3}
Steriruncicantellated 9-simplex

75600 15120
74

Template:CDD
t1,2,3,4{3,3,3,3,3,3,3,3}
Biruncicantitruncated 9-simplex

68040 15120
75

Template:CDD
t0,1,2,5{3,3,3,3,3,3,3,3}
Penticantitruncated 9-simplex

214200 25200
76

Template:CDD
t0,1,3,5{3,3,3,3,3,3,3,3}
Pentiruncitruncated 9-simplex

283500 37800
77

Template:CDD
t0,2,3,5{3,3,3,3,3,3,3,3}
Pentiruncicantellated 9-simplex

264600 37800
78

Template:CDD
t1,2,3,5{3,3,3,3,3,3,3,3}
Bistericantitruncated 9-simplex

245700 37800
79

Template:CDD
t0,1,4,5{3,3,3,3,3,3,3,3}
Pentisteritruncated 9-simplex

138600 25200
80

Template:CDD
t0,2,4,5{3,3,3,3,3,3,3,3}
Pentistericantellated 9-simplex

226800 37800
81

Template:CDD
t1,2,4,5{3,3,3,3,3,3,3,3}
Bisteriruncitruncated 9-simplex

189000 37800
82

Template:CDD
t0,3,4,5{3,3,3,3,3,3,3,3}
Pentisteriruncinated 9-simplex

138600 25200
83

Template:CDD
t1,3,4,5{3,3,3,3,3,3,3,3}
Bisteriruncicantellated 9-simplex

207900 37800
84

Template:CDD
t2,3,4,5{3,3,3,3,3,3,3,3}
Triruncicantitruncated 9-simplex

113400 25200
85

Template:CDD
t0,1,2,6{3,3,3,3,3,3,3,3}
Hexicantitruncated 9-simplex

226800 25200
86

Template:CDD
t0,1,3,6{3,3,3,3,3,3,3,3}
Hexiruncitruncated 9-simplex

453600 50400
87

Template:CDD
t0,2,3,6{3,3,3,3,3,3,3,3}
Hexiruncicantellated 9-simplex

403200 50400
88

Template:CDD
t1,2,3,6{3,3,3,3,3,3,3,3}
Bipenticantitruncated 9-simplex

378000 50400
89

Template:CDD
t0,1,4,6{3,3,3,3,3,3,3,3}
Hexisteritruncated 9-simplex

403200 50400
90

Template:CDD
t0,2,4,6{3,3,3,3,3,3,3,3}
Hexistericantellated 9-simplex

604800 75600
91

Template:CDD
t1,2,4,6{3,3,3,3,3,3,3,3}
Bipentiruncitruncated 9-simplex

529200 75600
92

Template:CDD
t0,3,4,6{3,3,3,3,3,3,3,3}
Hexisteriruncinated 9-simplex

352800 50400
93

Template:CDD
t1,3,4,6{3,3,3,3,3,3,3,3}
Bipentiruncicantellated 9-simplex

529200 75600
94

Template:CDD
t2,3,4,6{3,3,3,3,3,3,3,3}
Tristericantitruncated 9-simplex

302400 50400
95

Template:CDD
t0,1,5,6{3,3,3,3,3,3,3,3}
Hexipentitruncated 9-simplex

151200 25200
96

Template:CDD
t0,2,5,6{3,3,3,3,3,3,3,3}
Hexipenticantellated 9-simplex

352800 50400
97

Template:CDD
t1,2,5,6{3,3,3,3,3,3,3,3}
Bipentisteritruncated 9-simplex

277200 50400
98

Template:CDD
t0,3,5,6{3,3,3,3,3,3,3,3}
Hexipentiruncinated 9-simplex

352800 50400
99

Template:CDD
t1,3,5,6{3,3,3,3,3,3,3,3}
Bipentistericantellated 9-simplex

491400 75600
100

Template:CDD
t2,3,5,6{3,3,3,3,3,3,3,3}
Tristeriruncitruncated 9-simplex

252000 50400
101

Template:CDD
t0,4,5,6{3,3,3,3,3,3,3,3}
Hexipentistericated 9-simplex

151200 25200
102

Template:CDD
t1,4,5,6{3,3,3,3,3,3,3,3}
Bipentisteriruncinated 9-simplex

327600 50400
103

Template:CDD
t0,1,2,7{3,3,3,3,3,3,3,3}
Hepticantitruncated 9-simplex

128520 15120
104

Template:CDD
t0,1,3,7{3,3,3,3,3,3,3,3}
Heptiruncitruncated 9-simplex

359100 37800
105

Template:CDD
t0,2,3,7{3,3,3,3,3,3,3,3}
Heptiruncicantellated 9-simplex

302400 37800
106

Template:CDD
t1,2,3,7{3,3,3,3,3,3,3,3}
Bihexicantitruncated 9-simplex

283500 37800
107

Template:CDD
t0,1,4,7{3,3,3,3,3,3,3,3}
Heptisteritruncated 9-simplex

478800 50400
108

Template:CDD
t0,2,4,7{3,3,3,3,3,3,3,3}
Heptistericantellated 9-simplex

680400 75600
109

Template:CDD
t1,2,4,7{3,3,3,3,3,3,3,3}
Bihexiruncitruncated 9-simplex

604800 75600
110

Template:CDD
t0,3,4,7{3,3,3,3,3,3,3,3}
Heptisteriruncinated 9-simplex

378000 50400
111

Template:CDD
t1,3,4,7{3,3,3,3,3,3,3,3}
Bihexiruncicantellated 9-simplex

567000 75600
112

Template:CDD
t0,1,5,7{3,3,3,3,3,3,3,3}
Heptipentitruncated 9-simplex

321300 37800
113

Template:CDD
t0,2,5,7{3,3,3,3,3,3,3,3}
Heptipenticantellated 9-simplex

680400 75600
114

Template:CDD
t1,2,5,7{3,3,3,3,3,3,3,3}
Bihexisteritruncated 9-simplex

567000 75600
115

Template:CDD
t0,3,5,7{3,3,3,3,3,3,3,3}
Heptipentiruncinated 9-simplex

642600 75600
116

Template:CDD
t1,3,5,7{3,3,3,3,3,3,3,3}
Bihexistericantellated 9-simplex

907200 113400
117

Template:CDD
t0,4,5,7{3,3,3,3,3,3,3,3}
Heptipentistericated 9-simplex

264600 37800
118

Template:CDD
t0,1,6,7{3,3,3,3,3,3,3,3}
Heptihexitruncated 9-simplex

98280 15120
119

Template:CDD
t0,2,6,7{3,3,3,3,3,3,3,3}
Heptihexicantellated 9-simplex

302400 37800
120

Template:CDD
t1,2,6,7{3,3,3,3,3,3,3,3}
Bihexipentitruncated 9-simplex

226800 37800
121

Template:CDD
t0,3,6,7{3,3,3,3,3,3,3,3}
Heptihexiruncinated 9-simplex

428400 50400
122

Template:CDD
t0,4,6,7{3,3,3,3,3,3,3,3}
Heptihexistericated 9-simplex

302400 37800
123

Template:CDD
t0,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipentellated 9-simplex

98280 15120
124

Template:CDD
t0,1,2,8{3,3,3,3,3,3,3,3}
Octicantitruncated 9-simplex

35280 5040
125

Template:CDD
t0,1,3,8{3,3,3,3,3,3,3,3}
Octiruncitruncated 9-simplex

136080 15120
126

Template:CDD
t0,2,3,8{3,3,3,3,3,3,3,3}
Octiruncicantellated 9-simplex

105840 15120
127

Template:CDD
t0,1,4,8{3,3,3,3,3,3,3,3}
Octisteritruncated 9-simplex

252000 25200
128

Template:CDD
t0,2,4,8{3,3,3,3,3,3,3,3}
Octistericantellated 9-simplex

340200 37800
129

Template:CDD
t0,3,4,8{3,3,3,3,3,3,3,3}
Octisteriruncinated 9-simplex

176400 25200
130

Template:CDD
t0,1,5,8{3,3,3,3,3,3,3,3}
Octipentitruncated 9-simplex

252000 25200
131

Template:CDD
t0,2,5,8{3,3,3,3,3,3,3,3}
Octipenticantellated 9-simplex

504000 50400
132

Template:CDD
t0,3,5,8{3,3,3,3,3,3,3,3}
Octipentiruncinated 9-simplex

453600 50400
133

Template:CDD
t0,1,6,8{3,3,3,3,3,3,3,3}
Octihexitruncated 9-simplex

136080 15120
134

Template:CDD
t0,2,6,8{3,3,3,3,3,3,3,3}
Octihexicantellated 9-simplex

378000 37800
135

Template:CDD
t0,1,7,8{3,3,3,3,3,3,3,3}
Octiheptitruncated 9-simplex

35280 5040
136

Template:CDD
t0,1,2,3,4{3,3,3,3,3,3,3,3}
Steriruncicantitruncated 9-simplex

136080 30240
137

Template:CDD
t0,1,2,3,5{3,3,3,3,3,3,3,3}
Pentiruncicantitruncated 9-simplex

491400 75600
138

Template:CDD
t0,1,2,4,5{3,3,3,3,3,3,3,3}
Pentistericantitruncated 9-simplex

378000 75600
139

Template:CDD
t0,1,3,4,5{3,3,3,3,3,3,3,3}
Pentisteriruncitruncated 9-simplex

378000 75600
140

Template:CDD
t0,2,3,4,5{3,3,3,3,3,3,3,3}
Pentisteriruncicantellated 9-simplex

378000 75600
141

Template:CDD
t1,2,3,4,5{3,3,3,3,3,3,3,3}
Bisteriruncicantitruncated 9-simplex

340200 75600
142

Template:CDD
t0,1,2,3,6{3,3,3,3,3,3,3,3}
Hexiruncicantitruncated 9-simplex

756000 100800
143

Template:CDD
t0,1,2,4,6{3,3,3,3,3,3,3,3}
Hexistericantitruncated 9-simplex

1058400 151200
144

Template:CDD
t0,1,3,4,6{3,3,3,3,3,3,3,3}
Hexisteriruncitruncated 9-simplex

982800 151200
145

Template:CDD
t0,2,3,4,6{3,3,3,3,3,3,3,3}
Hexisteriruncicantellated 9-simplex

982800 151200
146

Template:CDD
t1,2,3,4,6{3,3,3,3,3,3,3,3}
Bipentiruncicantitruncated 9-simplex

907200 151200
147

Template:CDD
t0,1,2,5,6{3,3,3,3,3,3,3,3}
Hexipenticantitruncated 9-simplex

554400 100800
148

Template:CDD
t0,1,3,5,6{3,3,3,3,3,3,3,3}
Hexipentiruncitruncated 9-simplex

907200 151200
149

Template:CDD
t0,2,3,5,6{3,3,3,3,3,3,3,3}
Hexipentiruncicantellated 9-simplex

831600 151200
150

Template:CDD
t1,2,3,5,6{3,3,3,3,3,3,3,3}
Bipentistericantitruncated 9-simplex

756000 151200
151

Template:CDD
t0,1,4,5,6{3,3,3,3,3,3,3,3}
Hexipentisteritruncated 9-simplex

554400 100800
152

Template:CDD
t0,2,4,5,6{3,3,3,3,3,3,3,3}
Hexipentistericantellated 9-simplex

907200 151200
153

Template:CDD
t1,2,4,5,6{3,3,3,3,3,3,3,3}
Bipentisteriruncitruncated 9-simplex

756000 151200
154

Template:CDD
t0,3,4,5,6{3,3,3,3,3,3,3,3}
Hexipentisteriruncinated 9-simplex

554400 100800
155

Template:CDD
t1,3,4,5,6{3,3,3,3,3,3,3,3}
Bipentisteriruncicantellated 9-simplex

831600 151200
156

Template:CDD
t2,3,4,5,6{3,3,3,3,3,3,3,3}
Tristeriruncicantitruncated 9-simplex

453600 100800
157

Template:CDD
t0,1,2,3,7{3,3,3,3,3,3,3,3}
Heptiruncicantitruncated 9-simplex

567000 75600
158

Template:CDD
t0,1,2,4,7{3,3,3,3,3,3,3,3}
Heptistericantitruncated 9-simplex

1209600 151200
159

Template:CDD
t0,1,3,4,7{3,3,3,3,3,3,3,3}
Heptisteriruncitruncated 9-simplex

1058400 151200
160

Template:CDD
t0,2,3,4,7{3,3,3,3,3,3,3,3}
Heptisteriruncicantellated 9-simplex

1058400 151200
161

Template:CDD
t1,2,3,4,7{3,3,3,3,3,3,3,3}
Bihexiruncicantitruncated 9-simplex

982800 151200
162

Template:CDD
t0,1,2,5,7{3,3,3,3,3,3,3,3}
Heptipenticantitruncated 9-simplex

1134000 151200
163

Template:CDD
t0,1,3,5,7{3,3,3,3,3,3,3,3}
Heptipentiruncitruncated 9-simplex

1701000 226800
164

Template:CDD
t0,2,3,5,7{3,3,3,3,3,3,3,3}
Heptipentiruncicantellated 9-simplex

1587600 226800
165

Template:CDD
t1,2,3,5,7{3,3,3,3,3,3,3,3}
Bihexistericantitruncated 9-simplex

1474200 226800
166

Template:CDD
t0,1,4,5,7{3,3,3,3,3,3,3,3}
Heptipentisteritruncated 9-simplex

982800 151200
167

Template:CDD
t0,2,4,5,7{3,3,3,3,3,3,3,3}
Heptipentistericantellated 9-simplex

1587600 226800
168

Template:CDD
t1,2,4,5,7{3,3,3,3,3,3,3,3}
Bihexisteriruncitruncated 9-simplex

1360800 226800
169

Template:CDD
t0,3,4,5,7{3,3,3,3,3,3,3,3}
Heptipentisteriruncinated 9-simplex

982800 151200
170

Template:CDD
t1,3,4,5,7{3,3,3,3,3,3,3,3}
Bihexisteriruncicantellated 9-simplex

1474200 226800
171

Template:CDD
t0,1,2,6,7{3,3,3,3,3,3,3,3}
Heptihexicantitruncated 9-simplex

453600 75600
172

Template:CDD
t0,1,3,6,7{3,3,3,3,3,3,3,3}
Heptihexiruncitruncated 9-simplex

1058400 151200
173

Template:CDD
t0,2,3,6,7{3,3,3,3,3,3,3,3}
Heptihexiruncicantellated 9-simplex

907200 151200
174

Template:CDD
t1,2,3,6,7{3,3,3,3,3,3,3,3}
Bihexipenticantitruncated 9-simplex

831600 151200
175

Template:CDD
t0,1,4,6,7{3,3,3,3,3,3,3,3}
Heptihexisteritruncated 9-simplex

1058400 151200
176

Template:CDD
t0,2,4,6,7{3,3,3,3,3,3,3,3}
Heptihexistericantellated 9-simplex

1587600 226800
177

Template:CDD
t1,2,4,6,7{3,3,3,3,3,3,3,3}
Bihexipentiruncitruncated 9-simplex

1360800 226800
178

Template:CDD
t0,3,4,6,7{3,3,3,3,3,3,3,3}
Heptihexisteriruncinated 9-simplex

907200 151200
179

Template:CDD
t0,1,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipentitruncated 9-simplex

453600 75600
180

Template:CDD
t0,2,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipenticantellated 9-simplex

1058400 151200
181

Template:CDD
t0,3,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipentiruncinated 9-simplex

1058400 151200
182

Template:CDD
t0,4,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipentistericated 9-simplex

453600 75600
183

Template:CDD
t0,1,2,3,8{3,3,3,3,3,3,3,3}
Octiruncicantitruncated 9-simplex

196560 30240
184

Template:CDD
t0,1,2,4,8{3,3,3,3,3,3,3,3}
Octistericantitruncated 9-simplex

604800 75600
185

Template:CDD
t0,1,3,4,8{3,3,3,3,3,3,3,3}
Octisteriruncitruncated 9-simplex

491400 75600
186

Template:CDD
t0,2,3,4,8{3,3,3,3,3,3,3,3}
Octisteriruncicantellated 9-simplex

491400 75600
187

Template:CDD
t0,1,2,5,8{3,3,3,3,3,3,3,3}
Octipenticantitruncated 9-simplex

856800 100800
188

Template:CDD
t0,1,3,5,8{3,3,3,3,3,3,3,3}
Octipentiruncitruncated 9-simplex

1209600 151200
189

Template:CDD
t0,2,3,5,8{3,3,3,3,3,3,3,3}
Octipentiruncicantellated 9-simplex

1134000 151200
190

Template:CDD
t0,1,4,5,8{3,3,3,3,3,3,3,3}
Octipentisteritruncated 9-simplex

655200 100800
191

Template:CDD
t0,2,4,5,8{3,3,3,3,3,3,3,3}
Octipentistericantellated 9-simplex

1058400 151200
192

Template:CDD
t0,3,4,5,8{3,3,3,3,3,3,3,3}
Octipentisteriruncinated 9-simplex

655200 100800
193

Template:CDD
t0,1,2,6,8{3,3,3,3,3,3,3,3}
Octihexicantitruncated 9-simplex

604800 75600
194

Template:CDD
t0,1,3,6,8{3,3,3,3,3,3,3,3}
Octihexiruncitruncated 9-simplex

1285200 151200
195

Template:CDD
t0,2,3,6,8{3,3,3,3,3,3,3,3}
Octihexiruncicantellated 9-simplex

1134000 151200
196

Template:CDD
t0,1,4,6,8{3,3,3,3,3,3,3,3}
Octihexisteritruncated 9-simplex

1209600 151200
197

Template:CDD
t0,2,4,6,8{3,3,3,3,3,3,3,3}
Octihexistericantellated 9-simplex

1814400 226800
198

Template:CDD
t0,1,5,6,8{3,3,3,3,3,3,3,3}
Octihexipentitruncated 9-simplex

491400 75600
199

Template:CDD
t0,1,2,7,8{3,3,3,3,3,3,3,3}
Octihepticantitruncated 9-simplex

196560 30240
200

Template:CDD
t0,1,3,7,8{3,3,3,3,3,3,3,3}
Octiheptiruncitruncated 9-simplex

604800 75600
201

Template:CDD
t0,1,4,7,8{3,3,3,3,3,3,3,3}
Octiheptisteritruncated 9-simplex

856800 100800
202

Template:CDD
t0,1,2,3,4,5{3,3,3,3,3,3,3,3}
Pentisteriruncicantitruncated 9-simplex

680400 151200
203

Template:CDD
t0,1,2,3,4,6{3,3,3,3,3,3,3,3}
Hexisteriruncicantitruncated 9-simplex

1814400 302400
204

Template:CDD
t0,1,2,3,5,6{3,3,3,3,3,3,3,3}
Hexipentiruncicantitruncated 9-simplex

1512000 302400
205

Template:CDD
t0,1,2,4,5,6{3,3,3,3,3,3,3,3}
Hexipentistericantitruncated 9-simplex

1512000 302400
206

Template:CDD
t0,1,3,4,5,6{3,3,3,3,3,3,3,3}
Hexipentisteriruncitruncated 9-simplex

1512000 302400
207

Template:CDD
t0,2,3,4,5,6{3,3,3,3,3,3,3,3}
Hexipentisteriruncicantellated 9-simplex

1512000 302400
208

Template:CDD
t1,2,3,4,5,6{3,3,3,3,3,3,3,3}
Bipentisteriruncicantitruncated 9-simplex

1360800 302400
209

Template:CDD
t0,1,2,3,4,7{3,3,3,3,3,3,3,3}
Heptisteriruncicantitruncated 9-simplex

1965600 302400
210

Template:CDD
t0,1,2,3,5,7{3,3,3,3,3,3,3,3}
Heptipentiruncicantitruncated 9-simplex

2948400 453600
211

Template:CDD
t0,1,2,4,5,7{3,3,3,3,3,3,3,3}
Heptipentistericantitruncated 9-simplex

2721600 453600
212

Template:CDD
t0,1,3,4,5,7{3,3,3,3,3,3,3,3}
Heptipentisteriruncitruncated 9-simplex

2721600 453600
213

Template:CDD
t0,2,3,4,5,7{3,3,3,3,3,3,3,3}
Heptipentisteriruncicantellated 9-simplex

2721600 453600
214

Template:CDD
t1,2,3,4,5,7{3,3,3,3,3,3,3,3}
Bihexisteriruncicantitruncated 9-simplex

2494800 453600
215

Template:CDD
t0,1,2,3,6,7{3,3,3,3,3,3,3,3}
Heptihexiruncicantitruncated 9-simplex

1663200 302400
216

Template:CDD
t0,1,2,4,6,7{3,3,3,3,3,3,3,3}
Heptihexistericantitruncated 9-simplex

2721600 453600
217

Template:CDD
t0,1,3,4,6,7{3,3,3,3,3,3,3,3}
Heptihexisteriruncitruncated 9-simplex

2494800 453600
218

Template:CDD
t0,2,3,4,6,7{3,3,3,3,3,3,3,3}
Heptihexisteriruncicantellated 9-simplex

2494800 453600
219

Template:CDD
t1,2,3,4,6,7{3,3,3,3,3,3,3,3}
Bihexipentiruncicantitruncated 9-simplex

2268000 453600
220

Template:CDD
t0,1,2,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipenticantitruncated 9-simplex

1663200 302400
221

Template:CDD
t0,1,3,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipentiruncitruncated 9-simplex

2721600 453600
222

Template:CDD
t0,2,3,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipentiruncicantellated 9-simplex

2494800 453600
223

Template:CDD
t1,2,3,5,6,7{3,3,3,3,3,3,3,3}
Bihexipentistericantitruncated 9-simplex

2268000 453600
224

Template:CDD
t0,1,4,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipentisteritruncated 9-simplex

1663200 302400
225

Template:CDD
t0,2,4,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipentistericantellated 9-simplex

2721600 453600
226

Template:CDD
t0,3,4,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipentisteriruncinated 9-simplex

1663200 302400
227

Template:CDD
t0,1,2,3,4,8{3,3,3,3,3,3,3,3}
Octisteriruncicantitruncated 9-simplex

907200 151200
228

Template:CDD
t0,1,2,3,5,8{3,3,3,3,3,3,3,3}
Octipentiruncicantitruncated 9-simplex

2116800 302400
229

Template:CDD
t0,1,2,4,5,8{3,3,3,3,3,3,3,3}
Octipentistericantitruncated 9-simplex

1814400 302400
230

Template:CDD
t0,1,3,4,5,8{3,3,3,3,3,3,3,3}
Octipentisteriruncitruncated 9-simplex

1814400 302400
231

Template:CDD
t0,2,3,4,5,8{3,3,3,3,3,3,3,3}
Octipentisteriruncicantellated 9-simplex

1814400 302400
232

Template:CDD
t0,1,2,3,6,8{3,3,3,3,3,3,3,3}
Octihexiruncicantitruncated 9-simplex

2116800 302400
233

Template:CDD
t0,1,2,4,6,8{3,3,3,3,3,3,3,3}
Octihexistericantitruncated 9-simplex

3175200 453600
234

Template:CDD
t0,1,3,4,6,8{3,3,3,3,3,3,3,3}
Octihexisteriruncitruncated 9-simplex

2948400 453600
235

Template:CDD
t0,2,3,4,6,8{3,3,3,3,3,3,3,3}
Octihexisteriruncicantellated 9-simplex

2948400 453600
236

Template:CDD
t0,1,2,5,6,8{3,3,3,3,3,3,3,3}
Octihexipenticantitruncated 9-simplex

1814400 302400
237

Template:CDD
t0,1,3,5,6,8{3,3,3,3,3,3,3,3}
Octihexipentiruncitruncated 9-simplex

2948400 453600
238

Template:CDD
t0,2,3,5,6,8{3,3,3,3,3,3,3,3}
Octihexipentiruncicantellated 9-simplex

2721600 453600
239

Template:CDD
t0,1,4,5,6,8{3,3,3,3,3,3,3,3}
Octihexipentisteritruncated 9-simplex

1814400 302400
240

Template:CDD
t0,1,2,3,7,8{3,3,3,3,3,3,3,3}
Octiheptiruncicantitruncated 9-simplex

907200 151200
241

Template:CDD
t0,1,2,4,7,8{3,3,3,3,3,3,3,3}
Octiheptistericantitruncated 9-simplex

2116800 302400
242

Template:CDD
t0,1,3,4,7,8{3,3,3,3,3,3,3,3}
Octiheptisteriruncitruncated 9-simplex

1814400 302400
243

Template:CDD
t0,1,2,5,7,8{3,3,3,3,3,3,3,3}
Octiheptipenticantitruncated 9-simplex

2116800 302400
244

Template:CDD
t0,1,3,5,7,8{3,3,3,3,3,3,3,3}
Octiheptipentiruncitruncated 9-simplex

3175200 453600
245

Template:CDD
t0,1,2,6,7,8{3,3,3,3,3,3,3,3}
Octiheptihexicantitruncated 9-simplex

907200 151200
246

Template:CDD
t0,1,2,3,4,5,6{3,3,3,3,3,3,3,3}
Hexipentisteriruncicantitruncated 9-simplex

2721600 604800
247

Template:CDD
t0,1,2,3,4,5,7{3,3,3,3,3,3,3,3}
Heptipentisteriruncicantitruncated 9-simplex

4989600 907200
248

Template:CDD
t0,1,2,3,4,6,7{3,3,3,3,3,3,3,3}
Heptihexisteriruncicantitruncated 9-simplex

4536000 907200
249

Template:CDD
t0,1,2,3,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipentiruncicantitruncated 9-simplex

4536000 907200
250

Template:CDD
t0,1,2,4,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipentistericantitruncated 9-simplex

4536000 907200
251

Template:CDD
t0,1,3,4,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipentisteriruncitruncated 9-simplex

4536000 907200
252

Template:CDD
t0,2,3,4,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipentisteriruncicantellated 9-simplex

4536000 907200
253

Template:CDD
t1,2,3,4,5,6,7{3,3,3,3,3,3,3,3}
Bihexipentisteriruncicantitruncated 9-simplex

4082400 907200
254

Template:CDD
t0,1,2,3,4,5,8{3,3,3,3,3,3,3,3}
Octipentisteriruncicantitruncated 9-simplex

3326400 604800
255

Template:CDD
t0,1,2,3,4,6,8{3,3,3,3,3,3,3,3}
Octihexisteriruncicantitruncated 9-simplex

5443200 907200
256

Template:CDD
t0,1,2,3,5,6,8{3,3,3,3,3,3,3,3}
Octihexipentiruncicantitruncated 9-simplex

4989600 907200
257

Template:CDD
t0,1,2,4,5,6,8{3,3,3,3,3,3,3,3}
Octihexipentistericantitruncated 9-simplex

4989600 907200
258

Template:CDD
t0,1,3,4,5,6,8{3,3,3,3,3,3,3,3}
Octihexipentisteriruncitruncated 9-simplex

4989600 907200
259

Template:CDD
t0,2,3,4,5,6,8{3,3,3,3,3,3,3,3}
Octihexipentisteriruncicantellated 9-simplex

4989600 907200
260

Template:CDD
t0,1,2,3,4,7,8{3,3,3,3,3,3,3,3}
Octiheptisteriruncicantitruncated 9-simplex

3326400 604800
261

Template:CDD
t0,1,2,3,5,7,8{3,3,3,3,3,3,3,3}
Octiheptipentiruncicantitruncated 9-simplex

5443200 907200
262

Template:CDD
t0,1,2,4,5,7,8{3,3,3,3,3,3,3,3}
Octiheptipentistericantitruncated 9-simplex

4989600 907200
263

Template:CDD
t0,1,3,4,5,7,8{3,3,3,3,3,3,3,3}
Octiheptipentisteriruncitruncated 9-simplex

4989600 907200
264

Template:CDD
t0,1,2,3,6,7,8{3,3,3,3,3,3,3,3}
Octiheptihexiruncicantitruncated 9-simplex

3326400 604800
265

Template:CDD
t0,1,2,4,6,7,8{3,3,3,3,3,3,3,3}
Octiheptihexistericantitruncated 9-simplex

5443200 907200
266

Template:CDD
t0,1,2,3,4,5,6,7{3,3,3,3,3,3,3,3}
Heptihexipentisteriruncicantitruncated 9-simplex

8164800 1814400
267

Template:CDD
t0,1,2,3,4,5,6,8{3,3,3,3,3,3,3,3}
Octihexipentisteriruncicantitruncated 9-simplex

9072000 1814400
268

Template:CDD
t0,1,2,3,4,5,7,8{3,3,3,3,3,3,3,3}
Octiheptipentisteriruncicantitruncated 9-simplex

9072000 1814400
269

Template:CDD
t0,1,2,3,4,6,7,8{3,3,3,3,3,3,3,3}
Octiheptihexisteriruncicantitruncated 9-simplex

9072000 1814400
270

Template:CDD
t0,1,2,3,5,6,7,8{3,3,3,3,3,3,3,3}
Octiheptihexipentiruncicantitruncated 9-simplex

9072000 1814400
271

Template:CDD
t0,1,2,3,4,5,6,7,8{3,3,3,3,3,3,3,3}
Omnitruncated 9-simplex

16329600 3628800

The B9 family

There are 511 forms based on all permutations of the Coxeter-Dynkin diagrams with one or more rings.

Eleven cases are shown below: Nine rectified forms and 2 truncations. Bowers-style acronym names are given in parentheses for cross-referencing. Bowers-style acronym names are given in parentheses for cross-referencing.

# Graph Coxeter-Dynkin diagram
Schläfli symbol
Name 		Element counts
8-faces 7-faces 6-faces 5-faces 4-faces Cells Faces Edges Vertices
1 Template:CDD
t0{4,3,3,3,3,3,3,3}
9-cube (enne) 		18 144 672 2016 4032 5376 4608 2304 512
2 Template:CDD
t0,1{4,3,3,3,3,3,3,3}
Truncated 9-cube (ten) 		2304 4608
3 Template:CDD
t1{4,3,3,3,3,3,3,3}
Rectified 9-cube (ren) 		18432 2304
4 Template:CDD
t2{4,3,3,3,3,3,3,3}
Birectified 9-cube (barn) 		64512 4608
5 Template:CDD
t3{4,3,3,3,3,3,3,3}
Trirectified 9-cube (tarn) 		96768 5376
6 Template:CDD
t4{4,3,3,3,3,3,3,3}
Quadrirectified 9-cube (nav)
(Quadrirectified 9-orthoplex) 		80640 4032
7 Template:CDD
t3{3,3,3,3,3,3,3,4}
Trirectified 9-orthoplex (tarv) 		40320 2016
8 Template:CDD
t2{3,3,3,3,3,3,3,4}
Birectified 9-orthoplex (brav) 		12096 672
9 Template:CDD
t1{3,3,3,3,3,3,3,4}
Rectified 9-orthoplex (riv) 		2016 144
10 Template:CDD
t0,1{3,3,3,3,3,3,3,4}
Truncated 9-orthoplex (tiv) 		2160 288
11 Template:CDD
t0{3,3,3,3,3,3,3,4}
9-orthoplex (vee) 		512 2304 4608 5376 4032 2016 672 144 18

The D9 family

The D9 family has symmetry of order 92,897,280 (9 factorial × 28).

This family has 3×128−1=383 Wythoffian uniform polytopes, generated by marking one or more nodes of the D9 Coxeter-Dynkin diagram. Of these, 255 (2×128−1) are repeated from the B9 family and 128 are unique to this family, with the eight 1 or 2 ringed forms listed below. Bowers-style acronym names are given in parentheses for cross-referencing.

# Coxeter plane graphs Coxeter-Dynkin diagram
Schläfli symbol 		Base point
(Alternately signed) 		Element counts Circumrad
B9 D9 D8 D7 D6 D5 D4 D3 A7 A5 A3 8 7 6 5 4 3 2 1 0
1 Error creating thumbnail: File:9-demicube t0 A7.svg File:9-demicube t0 A5.svg File:9-demicube t0 A3.svg Template:CDD
9-demicube (henne)		 (1,1,1,1,1,1,1,1,1) 274 2448 9888 23520 36288 37632 21404 4608 256 1.0606601
2 File:9-demicube t01 B9.svg File:9-demicube t01 D9.svg File:9-demicube t01 D8.svg File:9-demicube t01 D7.svg File:9-demicube t01 D6.svg File:9-demicube t01 D5.svg File:9-demicube t01 D4.svg File:9-demicube t01 D3.svg File:9-demicube t01 A7.svg File:9-demicube t01 A5.svg File:9-demicube t01 A3.svg Template:CDD
Truncated 9-demicube (thenne)		 (1,1,3,3,3,3,3,3,3) 69120 9216 2.8504384
3 File:9-demicube t02 B9.svg File:9-demicube t02 D9.svg File:9-demicube t02 D8.svg File:9-demicube t02 D7.svg File:9-demicube t02 D6.svg File:9-demicube t02 D5.svg File:9-demicube t02 D4.svg File:9-demicube t02 D3.svg File:9-demicube t02 A7.svg File:9-demicube t02 A5.svg File:9-demicube t02 A3.svg Template:CDD
Cantellated 9-demicube		 (1,1,1,3,3,3,3,3,3) 225792 21504 2.6692696
4 File:9-demicube t03 B9.svg File:9-demicube t03 D9.svg File:9-demicube t03 D8.svg File:9-demicube t03 D7.svg File:9-demicube t03 D6.svg File:9-demicube t03 D5.svg File:9-demicube t03 D4.svg File:9-demicube t03 D3.svg File:9-demicube t03 A7.svg File:9-demicube t03 A5.svg File:9-demicube t03 A3.svg Template:CDD
Runcinated 9-demicube		 (1,1,1,1,3,3,3,3,3) 419328 32256 2.4748735
5 File:9-demicube t04 B9.svg File:9-demicube t04 D9.svg File:9-demicube t04 D8.svg File:9-demicube t04 D7.svg File:9-demicube t04 D6.svg File:9-demicube t04 D5.svg File:9-demicube t04 D4.svg File:9-demicube t04 D3.svg File:9-demicube t04 A7.svg File:9-demicube t04 A5.svg File:9-demicube t04 A3.svg Template:CDD
Stericated 9-demicube		 (1,1,1,1,1,3,3,3,3) 483840 32256 2.2638462
6 File:9-demicube t05 B9.svg File:9-demicube t05 D9.svg File:9-demicube t05 D8.svg File:9-demicube t05 D7.svg File:9-demicube t05 D6.svg File:9-demicube t05 D5.svg File:9-demicube t05 D4.svg File:9-demicube t05 D3.svg File:9-demicube t05 A7.svg File:9-demicube t05 A5.svg File:9-demicube t05 A3.svg Template:CDD
Pentellated 9-demicube		 (1,1,1,1,1,1,3,3,3) 354816 21504 2.0310094
7 File:9-demicube t06 B9.svg File:9-demicube t06 D9.svg File:9-demicube t06 D8.svg File:9-demicube t06 D7.svg File:9-demicube t06 D6.svg File:9-demicube t06 D5.svg File:9-demicube t06 D4.svg File:9-demicube t06 D3.svg File:9-demicube t06 A7.svg File:9-demicube t06 A5.svg File:9-demicube t06 A3.svg Template:CDD
Hexicated 9-demicube		 (1,1,1,1,1,1,1,3,3) 161280 9216 1.7677668
8 File:9-demicube t07 B9.svg File:9-demicube t07 D9.svg File:9-demicube t07 D8.svg File:9-demicube t07 D7.svg File:9-demicube t07 D6.svg File:9-demicube t07 D5.svg File:9-demicube t07 D4.svg File:9-demicube t07 D3.svg File:9-demicube t07 A7.svg File:9-demicube t07 A5.svg Template:CDD
Heptellated 9-demicube		 (1,1,1,1,1,1,1,1,3) 41472 2304 1.4577379

Regular and uniform honeycombs

Coxeter-Dynkin diagram correspondences between families and higher symmetry within diagrams. Nodes of the same color in each row represent identical mirrors. Black nodes are not active in the correspondence.

There are five fundamental affine Coxeter groups that generate regular and uniform tessellations in 8-space:

# Coxeter group Coxeter diagram Forms
1 A~8 [3[9]] Template:CDD 45
2 C~8 [4,36,4] Template:CDD 271
3 B~8 h[4,36,4]
[4,35,31,1]		 Template:CDD 383 (128 new)
4 D~8 q[4,36,4]
[31,1,34,31,1]		 Template:CDD 155 (15 new)
5 E~8 [35,2,1] Template:CDD 511

Regular and uniform tessellations include:

Regular and uniform hyperbolic honeycombs

There are no compact hyperbolic Coxeter groups of rank 9, groups that can generate honeycombs with all finite facets, and a finite vertex figure. However there are 4 noncompact hyperbolic Coxeter groups of rank 9, each generating uniform honeycombs in 8-space as permutations of rings of the Coxeter diagrams.

P¯8 = [3,3[8]]:
Template:CDD 		Q¯8 = [31,1,33,32,1]:
Template:CDD 		S¯8 = [4,34,32,1]:
Template:CDD 		T¯8 = [34,3,1]:
Template:CDD

References

  • T. Gosset: On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900
  • A. Boole Stott: Geometrical deduction of semiregular from regular polytopes and space fillings, Verhandelingen of the Koninklijke academy van Wetenschappen width unit Amsterdam, Eerste Sectie 11,1, Amsterdam, 1910
  • H.S.M. Coxeter:
    • H.S.M. Coxeter, M.S. Longuet-Higgins und J.C.P. Miller: Uniform Polyhedra, Philosophical Transactions of the Royal Society of London, Londne, 1954
    • H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
  • Kaleidoscopes: Selected Writings of H.S.M. Coxeter, editied by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
    • (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
    • (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
    • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
  • N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
  • Template:KlitzingPolytopes

Template:Polytopes (I'm no baseball guy, but if you increase the opponent's chance of winning by intentionally putting a runner on first in that situation, how come EVERY manager does it?
The citizens of Summerside and the surrounding area derserved this facility, for too long we had to use outdated decrepit, unsafe and embarassing facilities, I applaud ethe Mayor and the Council at the time who had the vision, and the and the community spirit to push the building of this facility thru all the politics and legal stuff to get this built. And it continues to grow, The addition of a the skateboarding facility tp CUP is proving to be a well used and appreciated park for our young citizens.
http://southfloridanfp.org/coach/?key=cheap-coach-outlet-24
http://southfloridanfp.org/coach/?key=coach-gilroy-outlet-90
http://southfloridanfp.org/coach/?key=coach-sneakers-outlet-25
http://southfloridanfp.org/coach/?key=coach-bags-on-sale-at-outlet-33
http://southfloridanfp.org/coach/?key=coach-pocketbooks-outlet-64


If you adored this post and you would certainly such as to receive additional facts concerning Cheap Uggs Boots kindly go to the web site.

Retrieved from "https://en.formulasearchengine.com/w/index.php?title=Product_metric&oldid=14928"