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I make the selection of obtaining the 4 piece knife set rather of the six piece one.  The Wusthof classic knife set in this steak knife set are the precise similar knife.<br><br>It weighs nine pounds - a decent weight for such a extensive set - and measures 17.7×11.2×15 inches, little enough to match in a corner but substantial adequate to look the element. It has to be mentioned that OXO has carried out a good job in picking out these blades, despite the fact that some users have said they added extra knives from the OXO range to raise the versatility of the set. IMO there's no totally free lunch in the knife small business.<br><br>For that reason when contemplating the size of the knife set you need to have figure out what forms of actions you do routinely in the kitchen and think about a set that meets those wants.  The letters following the X number are the other elements in the knife and that number is the percentage that these components take up. 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Empty knife blocks in Cutlery - Compare Costs, Study Reviews and.. Friedr.<br><br>Set the table so that all the guests are comfortable and have every little thing they need.  The Joy of Cooking has an simple to comply with, timeless reference for formal and casual directions on how to set a table. To begin with the most fundamental should-have kitchen tools and gear, I generally recommend a good set of mixing bowls.  I advise this set of bowls by OXO Fantastic Grips mainly because they also have a non-skid bottom.<br><br>The Gourmet Steak Knife Set with Wood Case from Henckels (set of eight) ($79.95) are produced of high-carbon stainless steel in Germany and function the classic black-handled, triple riveted design. If you've currently got a set of German steel in a knife block, these knives will match them nicely. When buying for ceramic knife free of charge shipping critiques , you really should pay additional interest to the details.
{| class=wikitable align=right width=480
|- align=center valign=top
|[[File:5-cube t0.svg|160px]]<BR><small>[[5-cube]]</small><BR>{{CDD|node_1|4|node|3|node|3|node|3|node}}
|[[File:5-cube t04.svg|160px]]<BR><small>Stericated 5-cube</small><BR>{{CDD|node_1|4|node|3|node|3|node|3|node_1}}
|[[File:5-cube t014.svg|160px]]<BR><small>Steritruncated 5-cube</small><BR>{{CDD|node_1|4|node_1|3|node|3|node|3|node_1}}
|- align=center valign=top
|[[File:5-cube t024.svg|160px]]<BR><small>Stericantellated 5-cube</small><BR>{{CDD|node_1|4|node|3|node_1|3|node|3|node_1}}
|[[File:5-cube t034.svg|160px]]<BR><small>[[Steritruncated 5-orthoplex]]</small><BR>{{CDD|node_1|4|node|3|node|3|node_1|3|node_1}}
|[[File:5-cube t0124.svg|160px]]<BR><small>Stericantitruncated 5-cube</small><BR>{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1}}
|- align=center valign=top
|[[File:5-cube t0134.svg|160px]]<BR><small>Steriruncitruncated 5-cube</small><BR>{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1}}
|[[File:5-cube t0234.svg|160px]]<BR><small>[[Stericantitruncated 5-orthoplex]]</small><BR>{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1}}
|[[File:5-cube t01234.svg|160px]]<BR>[[Omnitruncated 5-cube]]<BR>{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1}}
|-
!colspan=3|[[Orthogonal projection]]s in BC<sub>5</sub> [[Coxeter plane]]
|}
In [[Five-dimensional space|five-dimensional]] [[geometry]], a '''stericated 5-cube''' is a convex [[uniform 5-polytope]] with fourth-order [[Truncation (geometry)|truncations]] ([[sterication]]) of the regular [[5-cube]].
 
There are eight degrees of sterication for the 5-cube, including permutations of runcination, cantellation, and truncation. The simple stericated 5-cube is also called an '''expanded 5-cube''', with the first and last nodes ringed, for being [[constructible polygon|constructible]] by an [[Expansion (geometry)|expansion]] operation applied to the regular 5-cube. The highest form, the '''steriruncicantitruncated 5-cube''', is more simply called an [[#Omnitruncated 5-cube|omnitruncated 5-cube]] with all of the nodes ringed.
 
== Stericated 5-cube ==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
|-
|bgcolor=#e7dcc3 align=center colspan=3|'''Stericated 5-cube'''
|-
|bgcolor=#e7dcc3|Type
|colspan=2|[[Uniform 5-polytope]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]
|colspan=2| 2r2r{4,3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]
|colspan=2|{{CDD||node_1|4|node||3|node|3|node|3|node_1}}<BR>{{CDD|node|split1|nodes|3a4b|nodes_11}}
|-
|bgcolor=#e7dcc3|4-faces
|242
|-
|bgcolor=#e7dcc3|Cells
|800
|-
|bgcolor=#e7dcc3|Faces
|1040
|-
|bgcolor=#e7dcc3|Edges
|640
|-
|bgcolor=#e7dcc3|Vertices
|160
|-
|bgcolor=#e7dcc3|[[Vertex figure]]
|colspan=2|[[File:Stericated penteract verf.png|80px]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]
|colspan=2| BC<sub>5</sub> [4,3,3,3]
|-
|bgcolor=#e7dcc3|Properties
|colspan=2|[[Convex polytope|convex]]
|}
 
=== Alternate names ===
* Stericated penteract / Stericated 5-orthoplex / Stericated pentacross
* Expanded penteract / Expanded 5-orthoplex / Expanded pentacross
* Small cellated penteract (Acronym: scan) (Jonathan Bowers)<ref>Klitzing, (x3o3o3o4x - scan)</ref>
 
=== Coordinates ===
The [[Cartesian coordinate]]s of the vertices of a ''stericated 5-cube'' having edge length&nbsp;2 are all permutations of:
 
:<math>\left(\pm1,\ \pm1,\ \pm1,\ \pm1,\ \pm(1+\sqrt{2})\right)</math>
 
=== Images ===
The stericated 5-cube is constructed by a [[sterication]] operation applied to the 5-cube.
 
{{5-cube Coxeter plane graphs|t04|150}}
 
==Steritruncated 5-cube==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
!bgcolor=#e7dcc3 colspan=2|Steritruncated 5-cube
|-
|bgcolor=#e7dcc3|Type||[[uniform polyteron]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]|| t<sub>0,1,4</sub>{4,3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]s||{{CDD|node_1|4|node_1|3|node|3|node|3|node_1}}
|-
|bgcolor=#e7dcc3|4-faces||242
|-
|bgcolor=#e7dcc3|Cells||1600
|-
|bgcolor=#e7dcc3|Faces||2960
|-
|bgcolor=#e7dcc3|Edges||2240
|-
|bgcolor=#e7dcc3|Vertices||640
|-
|bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Steritruncated 5-cube verf.png|80px]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]s||BC<sub>5</sub>, [3,3,3,4]
|-
|bgcolor=#e7dcc3|Properties||[[Convex polytope|convex]]
|}
 
===Alternate names===
* Steritruncated penteract
* Prismatotruncated penteract (Acronym: capt) (Jonathan Bowers)<ref>Klitzing, (x3o3o3x4x - capt)</ref>
 
===Construction and coordinates===
 
The [[Cartesian coordinate]]s of the vertices of a ''steritruncated 5-cube'' having edge length&nbsp;2 are all permutations of:
 
:<math>\left(\pm1,\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2}),\ \pm(1+2\sqrt{2})\right)</math>
 
=== Images ===
 
{{5-cube Coxeter plane graphs|t014|150}}
 
==Stericantellated 5-cube==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
|-
|bgcolor=#e7dcc3 align=center colspan=3|'''Stericantellated 5-cube'''
|-
|bgcolor=#e7dcc3|Type
|colspan=2|[[Uniform 5-polytope]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]
|colspan=2| 2r2r{4,3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]
|colspan=2|{{CDD||node_1|4|node|3|node_1|3|node|3|node_1}}<BR>{{CDD|node_1|split1|nodes|3a4b|nodes_11}}
|-
|bgcolor=#e7dcc3|4-faces||242
|-
|bgcolor=#e7dcc3|Cells||2080
|-
|bgcolor=#e7dcc3|Faces||4720
|-
|bgcolor=#e7dcc3|Edges||3840
|-
|bgcolor=#e7dcc3|Vertices||960
|-
|bgcolor=#e7dcc3|[[Vertex figure]]
|colspan=2|[[File:Stericantellated 5-cube verf.png|80px]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]
|colspan=2| BC<sub>5</sub> [4,3,3,3]
|-
|bgcolor=#e7dcc3|Properties
|colspan=2|[[Convex polytope|convex]]
|}
 
=== Alternate names ===
* Stericantellated penteract
* Stericantellated 5-orthoplex, stericantellated pentacross
* Cellirhombated penteractitriacontiditeron (Acronym: carnit) (Jonathan Bowers)<ref>Klitzing, (x3o3x3o4x - carnit)</ref>
 
=== Coordinates ===
The [[Cartesian coordinate]]s of the vertices of a ''stericantellated 5-cube'' having edge length&nbsp;2 are all permutations of:
 
:<math>\left(\pm1,\ \pm1,\ \pm1,\ \pm(1+\sqrt{2}),\ \pm(1+2\sqrt{2})\right)</math>
 
=== Images ===
 
{{5-cube Coxeter plane graphs|t024|150}}
 
==Stericantitruncated 5-cube==
{| class="wikitable" align="right" style="margin-left:10px" width="280"
|-
|bgcolor=#e7dcc3 align=center colspan=3|'''Stericantitruncated 5-cube'''
|-
|bgcolor=#e7dcc3|Type
|[[Uniform 5-polytope]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]
|t<sub>0,1,2,4</sub>{4,3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram|Coxeter-Dynkin<BR>diagram]]
|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1}}
|-
|bgcolor=#e7dcc3|4-faces||242
|-
|bgcolor=#e7dcc3|Cells||2400
|-
|bgcolor=#e7dcc3|Faces||6000
|-
|bgcolor=#e7dcc3|Edges||5760
|-
|bgcolor=#e7dcc3|Vertices||1920
|-
|bgcolor=#e7dcc3|[[Vertex figure]]
|colspan=2|[[File:Stericanitruncated 5-cube verf.png|80px]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]
|colspan=2| BC<sub>5</sub> [4,3,3,3]
|-
|bgcolor=#e7dcc3|Properties
|[[Convex polytope|convex]], [[isogonal figure|isogonal]]
|}
 
=== Alternate names ===
* Stericantitruncated penteract
* Steriruncicantellated 16-cell / Biruncicantitruncated pentacross
* Celligreatorhombated penteract (cogrin) (Jonathan Bowers)<ref>Klitzing, (x3o3x3x4x - cogrin)</ref>
 
=== Coordinates ===
The [[Cartesian coordinate]]s of the vertices of an stericantitruncated 5-cube having an edge length of&nbsp;2 are given by all permutations of coordinates and sign of:
 
:<math>\left(1,\ 1+\sqrt{2},\ 1+2\sqrt{2},\ 1+2\sqrt{2},\ 1+3\sqrt{2}\right)</math>
 
=== Images ===
{{5-cube Coxeter plane graphs|t013|150}}
 
==Steriruncitruncated 5-cube==
{| class="wikitable" align="right" style="margin-left:10px" width="280"
|-
|bgcolor=#e7dcc3 align=center colspan=3|'''Steriruncitruncated 5-cube'''
|-
|bgcolor=#e7dcc3|Type
|[[Uniform 5-polytope]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]
|2t2r{4,3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram|Coxeter-Dynkin<BR>diagram]]
|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1}}<BR>{{CDD|node|split1|nodes_11|3a4b|nodes_11}}
|-
|bgcolor=#e7dcc3|4-faces||242
|-
|bgcolor=#e7dcc3|Cells||2160
|-
|bgcolor=#e7dcc3|Faces||5760
|-
|bgcolor=#e7dcc3|Edges||5760
|-
|bgcolor=#e7dcc3|Vertices||1920
|-
|bgcolor=#e7dcc3|[[Vertex figure]]
|colspan=2|[[File:Steriruncitruncated 5-cube verf.png|80px]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]
|colspan=2| BC<sub>5</sub> [4,3,3,3]
|-
|bgcolor=#e7dcc3|Properties
|[[Convex polytope|convex]], [[isogonal]]
|}
 
=== Alternate names ===
* Steriruncitruncated penteract / Steriruncitruncated 5-orthoplex / Steriruncitruncated pentacross
* Celliprismatotruncated penteractitriacontiditeron  (captint) (Jonathan Bowers)<ref>Klitzing, (x3x3o3x4x - captint)</ref>
 
=== Coordinates ===
The [[Cartesian coordinate]]s of the vertices of an steriruncitruncated penteract having an edge length of&nbsp;2 are given by all permutations of coordinates and sign of:
 
:<math>\left(1,\ 1+\sqrt{2},\ 1+1\sqrt{2},\ 1+2\sqrt{2},\ 1+3\sqrt{2}\right)</math>
 
=== Images ===
{{5-cube Coxeter plane graphs|t0134|150}}
 
==Steritruncated 5-orthoplex==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
!bgcolor=#e7dcc3 colspan=2|Steritruncated 5-orthoplex
|-
|bgcolor=#e7dcc3|Type||[[uniform polyteron]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]|| t<sub>0,1,4</sub>{3,3,3,4}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]s||{{CDD|node_1|4|node|3|node|3|node_1|3|node_1}}
|-
|bgcolor=#e7dcc3|4-faces||242
|-
|bgcolor=#e7dcc3|Cells||1520
|-
|bgcolor=#e7dcc3|Faces||2880
|-
|bgcolor=#e7dcc3|Edges||2240
|-
|bgcolor=#e7dcc3|Vertices||640
|-
|bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Steritruncated 5-orthoplex verf.png|80px]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]||BC<sub>5</sub>, [3,3,3,4]
|-
|bgcolor=#e7dcc3|Properties||[[Convex polytope|convex]]
|}
 
===Alternate names===
* Steritruncated pentacross
* Celliprismated penteract (Acronym: cappin) (Jonathan Bowers)<ref>Klitzing, (x3x3o3o4x - cappin)</ref>
 
=== Coordinates ===
[[Cartesian coordinates]] for the vertices of a steritruncated 5-orthoplex, centered at the origin, are all [[permutation]]s of
:<math>\left(\pm1,\ \pm1,\ \pm1,\ \pm1,\ \pm(1+\sqrt{2})\right)</math>
 
=== Images ===
{{5-cube Coxeter plane graphs|t034|150}}
 
==Stericantitruncated 5-orthoplex==
{| class="wikitable" align="right" style="margin-left:10px" width="280"
|-
|bgcolor=#e7dcc3 align=center colspan=3|'''Stericantitruncated 5-orthoplex'''
|-
|bgcolor=#e7dcc3|Type
|[[Uniform 5-polytope]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]
|t<sub>0,2,3,4</sub>{4,3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram|Coxeter-Dynkin<BR>diagram]]
|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1}}
|-
|bgcolor=#e7dcc3|4-faces||242
|-
|bgcolor=#e7dcc3|Cells||2320
|-
|bgcolor=#e7dcc3|Faces||5920
|-
|bgcolor=#e7dcc3|Edges||5760
|-
|bgcolor=#e7dcc3|Vertices||1920
|-
|bgcolor=#e7dcc3|[[Vertex figure]]
|colspan=2|[[File:Stericanitruncated 5-orthoplex verf.png|80px]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]
|colspan=2| BC<sub>5</sub> [4,3,3,3]
|-
|bgcolor=#e7dcc3|Properties
|[[Convex polytope|convex]], [[isogonal]]
|}
 
=== Alternate names ===
* Stericantitruncated pentacross
* Celligreatorhombated pentacross (cogart) (Jonathan Bowers)<ref>Klitzing, (x3x3x3o4x - cogart)</ref>
 
=== Coordinates ===
The [[Cartesian coordinate]]s of the vertices of an stericantitruncated 5-orthoplex having an edge length of&nbsp;2 are given by all permutations of coordinates and sign of:
 
:<math>\left(1,\ 1,\ 1+\sqrt{2},\ 1+2\sqrt{2},\ 1+3\sqrt{2}\right)</math>
 
=== Images ===
{{5-cube Coxeter plane graphs|t0234|150}}
 
==Omnitruncated 5-cube==
{| class="wikitable" align="right" style="margin-left:10px" width="280"
|-
|bgcolor=#e7dcc3 align=center colspan=3|'''Omnitruncated 5-cube'''
|-
|bgcolor=#e7dcc3|Type
|[[Uniform 5-polytope]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]
|tr2r{4,3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram|Coxeter-Dynkin<BR>diagram]]
|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1}}<BR>{{CDD|node_1|split1|nodes_11|3a4b|nodes_11}}
|-
|bgcolor=#e7dcc3|4-faces||242
|-
|bgcolor=#e7dcc3|Cells||2640
|-
|bgcolor=#e7dcc3|Faces||8160
|-
|bgcolor=#e7dcc3|Edges||9600
|-
|bgcolor=#e7dcc3|Vertices||3840
|-
|bgcolor=#e7dcc3|[[Vertex figure]]
|colspan=2|[[File:Omnitruncated 5-cube verf.png|80px]]<BR>irr. {3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter group]]
|colspan=2| BC<sub>5</sub> [4,3,3,3]
|-
|bgcolor=#e7dcc3|Properties
|[[Convex polytope|convex]], [[isogonal]]
|}
 
=== Alternate names ===
* Steriruncicantitruncated 5-cube (Full expansion of [[omnitruncation]] for 5-polytopes by Johnson)
* Omnitruncated penteract
* Omnitruncated 16-cell / omnitruncated pentacross
* Great cellated penteractitriacontiditeron (Jonathan Bowers)<ref>Klitzing, (x3x3x3x4x - gacnet)</ref>
 
=== Coordinates ===
The [[Cartesian coordinate]]s of the vertices of an omnitruncated tesseract having an edge length of&nbsp;2 are given by all permutations of coordinates and sign of:
 
:<math>\left(1,\ 1+\sqrt{2},\ 1+2\sqrt{2},\ 1+3\sqrt{2},\ 1+4\sqrt{2}\right)</math>
 
=== Images ===
{{5-cube Coxeter plane graphs|t01234|150}}
 
== Related polytopes ==
This polytope is one of 31 [[Uniform_polyteron#Uniform_polyteron|uniform polytera]] generated from the regular [[5-cube]] or [[5-orthoplex]].
 
{{Penteract family}}
 
==Notes==
{{reflist}}
 
== References ==
* [[Harold Scott MacDonald Coxeter|H.S.M. Coxeter]]:
** 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)|Norman Johnson]] ''Uniform Polytopes'', Manuscript (1991)
** N.W. Johnson: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D.
* {{KlitzingPolytopes|polytera.htm|5D|uniform polytopes (polytera)}} x3o3o3o4x - scan, x3o3o3x4x - capt, x3o3x3o4x - carnit, x3o3x3x4x - cogrin, x3x3o3x4x - captint, x3x3x3x4x - gacnet, x3x3x3o4x - cogart
 
== External links ==
* {{PolyCell | urlname = glossary.html#simplex| title = Glossary for hyperspace}}
* [http://www.polytope.net/hedrondude/topes.htm Polytopes of Various Dimensions], Jonathan Bowers
* [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]
 
{{Polytopes}}
 
[[Category:5-polytopes]]

Revision as of 00:07, 16 July 2013

File:5-cube t0.svg
5-cube
Template:CDD 		File:5-cube t04.svg
Stericated 5-cube
Template:CDD 		File:5-cube t014.svg
Steritruncated 5-cube
Template:CDD
File:5-cube t024.svg
Stericantellated 5-cube
Template:CDD 		File:5-cube t034.svg
Steritruncated 5-orthoplex
Template:CDD 		File:5-cube t0124.svg
Stericantitruncated 5-cube
Template:CDD
File:5-cube t0134.svg
Steriruncitruncated 5-cube
Template:CDD 		File:5-cube t0234.svg
Stericantitruncated 5-orthoplex
Template:CDD 		File:5-cube t01234.svg
Omnitruncated 5-cube
Template:CDD
Orthogonal projections in BC5 Coxeter plane

In five-dimensional geometry, a stericated 5-cube is a convex uniform 5-polytope with fourth-order truncations (sterication) of the regular 5-cube.

There are eight degrees of sterication for the 5-cube, including permutations of runcination, cantellation, and truncation. The simple stericated 5-cube is also called an expanded 5-cube, with the first and last nodes ringed, for being constructible by an expansion operation applied to the regular 5-cube. The highest form, the steriruncicantitruncated 5-cube, is more simply called an omnitruncated 5-cube with all of the nodes ringed.

Stericated 5-cube

Stericated 5-cube
Type Uniform 5-polytope
Schläfli symbol 2r2r{4,3,3,3}
Coxeter-Dynkin diagram Template:CDD
Template:CDD
4-faces 242
Cells 800
Faces 1040
Edges 640
Vertices 160
Vertex figure File:Stericated penteract verf.png
Coxeter group BC5 [4,3,3,3]
Properties convex

Alternate names

  • Stericated penteract / Stericated 5-orthoplex / Stericated pentacross
  • Expanded penteract / Expanded 5-orthoplex / Expanded pentacross
  • Small cellated penteract (Acronym: scan) (Jonathan Bowers)[1]

Coordinates

The Cartesian coordinates of the vertices of a stericated 5-cube having edge length 2 are all permutations of:

(±1, ±1, ±1, ±1, ±(1+2))

Images

The stericated 5-cube is constructed by a sterication operation applied to the 5-cube.

Template:5-cube Coxeter plane graphs

Steritruncated 5-cube

Steritruncated 5-cube
Type uniform polyteron
Schläfli symbol t0,1,4{4,3,3,3}
Coxeter-Dynkin diagrams Template:CDD
4-faces 242
Cells 1600
Faces 2960
Edges 2240
Vertices 640
Vertex figure File:Steritruncated 5-cube verf.png
Coxeter groups BC5, [3,3,3,4]
Properties convex

Alternate names

  • Steritruncated penteract
  • Prismatotruncated penteract (Acronym: capt) (Jonathan Bowers)[2]

Construction and coordinates

The Cartesian coordinates of the vertices of a steritruncated 5-cube having edge length 2 are all permutations of:

(±1, ±(1+2), ±(1+2), ±(1+2), ±(1+22))

Images

Template:5-cube Coxeter plane graphs

Stericantellated 5-cube

Stericantellated 5-cube
Type Uniform 5-polytope
Schläfli symbol 2r2r{4,3,3,3}
Coxeter-Dynkin diagram Template:CDD
Template:CDD
4-faces 242
Cells 2080
Faces 4720
Edges 3840
Vertices 960
Vertex figure File:Stericantellated 5-cube verf.png
Coxeter group BC5 [4,3,3,3]
Properties convex

Alternate names

  • Stericantellated penteract
  • Stericantellated 5-orthoplex, stericantellated pentacross
  • Cellirhombated penteractitriacontiditeron (Acronym: carnit) (Jonathan Bowers)[3]

Coordinates

The Cartesian coordinates of the vertices of a stericantellated 5-cube having edge length 2 are all permutations of:

(±1, ±1, ±1, ±(1+2), ±(1+22))

Images

Template:5-cube Coxeter plane graphs

Stericantitruncated 5-cube

Stericantitruncated 5-cube
Type Uniform 5-polytope
Schläfli symbol t0,1,2,4{4,3,3,3}
Coxeter-Dynkin
diagram 		Template:CDD
4-faces 242
Cells 2400
Faces 6000
Edges 5760
Vertices 1920
Vertex figure File:Stericanitruncated 5-cube verf.png
Coxeter group BC5 [4,3,3,3]
Properties convex, isogonal

Alternate names

  • Stericantitruncated penteract
  • Steriruncicantellated 16-cell / Biruncicantitruncated pentacross
  • Celligreatorhombated penteract (cogrin) (Jonathan Bowers)[4]

Coordinates

The Cartesian coordinates of the vertices of an stericantitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of:

(1, 1+2, 1+22, 1+22, 1+32)

Images

Template:5-cube Coxeter plane graphs

Steriruncitruncated 5-cube

Steriruncitruncated 5-cube
Type Uniform 5-polytope
Schläfli symbol 2t2r{4,3,3,3}
Coxeter-Dynkin
diagram 		Template:CDD
Template:CDD
4-faces 242
Cells 2160
Faces 5760
Edges 5760
Vertices 1920
Vertex figure File:Steriruncitruncated 5-cube verf.png
Coxeter group BC5 [4,3,3,3]
Properties convex, isogonal

Alternate names

  • Steriruncitruncated penteract / Steriruncitruncated 5-orthoplex / Steriruncitruncated pentacross
  • Celliprismatotruncated penteractitriacontiditeron (captint) (Jonathan Bowers)[5]

Coordinates

The Cartesian coordinates of the vertices of an steriruncitruncated penteract having an edge length of 2 are given by all permutations of coordinates and sign of:

(1, 1+2, 1+12, 1+22, 1+32)

Images

Template:5-cube Coxeter plane graphs

Steritruncated 5-orthoplex

Steritruncated 5-orthoplex
Type uniform polyteron
Schläfli symbol t0,1,4{3,3,3,4}
Coxeter-Dynkin diagrams Template:CDD
4-faces 242
Cells 1520
Faces 2880
Edges 2240
Vertices 640
Vertex figure File:Steritruncated 5-orthoplex verf.png
Coxeter group BC5, [3,3,3,4]
Properties convex

Alternate names

  • Steritruncated pentacross
  • Celliprismated penteract (Acronym: cappin) (Jonathan Bowers)[6]

Coordinates

Cartesian coordinates for the vertices of a steritruncated 5-orthoplex, centered at the origin, are all permutations of

(±1, ±1, ±1, ±1, ±(1+2))

Images

Template:5-cube Coxeter plane graphs

Stericantitruncated 5-orthoplex

Stericantitruncated 5-orthoplex
Type Uniform 5-polytope
Schläfli symbol t0,2,3,4{4,3,3,3}
Coxeter-Dynkin
diagram 		Template:CDD
4-faces 242
Cells 2320
Faces 5920
Edges 5760
Vertices 1920
Vertex figure File:Stericanitruncated 5-orthoplex verf.png
Coxeter group BC5 [4,3,3,3]
Properties convex, isogonal

Alternate names

  • Stericantitruncated pentacross
  • Celligreatorhombated pentacross (cogart) (Jonathan Bowers)[7]

Coordinates

The Cartesian coordinates of the vertices of an stericantitruncated 5-orthoplex having an edge length of 2 are given by all permutations of coordinates and sign of:

(1, 1, 1+2, 1+22, 1+32)

Images

Template:5-cube Coxeter plane graphs

Omnitruncated 5-cube

Omnitruncated 5-cube
Type Uniform 5-polytope
Schläfli symbol tr2r{4,3,3,3}
Coxeter-Dynkin
diagram 		Template:CDD
Template:CDD
4-faces 242
Cells 2640
Faces 8160
Edges 9600
Vertices 3840
Vertex figure File:Omnitruncated 5-cube verf.png
irr. {3,3,3}
Coxeter group BC5 [4,3,3,3]
Properties convex, isogonal

Alternate names

  • Steriruncicantitruncated 5-cube (Full expansion of omnitruncation for 5-polytopes by Johnson)
  • Omnitruncated penteract
  • Omnitruncated 16-cell / omnitruncated pentacross
  • Great cellated penteractitriacontiditeron (Jonathan Bowers)[8]

Coordinates

The Cartesian coordinates of the vertices of an omnitruncated tesseract having an edge length of 2 are given by all permutations of coordinates and sign of:

(1, 1+2, 1+22, 1+32, 1+42)

Images

Template:5-cube Coxeter plane graphs

This polytope is one of 31 uniform polytera generated from the regular 5-cube or 5-orthoplex.

Template:Penteract family

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

References

  • H.S.M. Coxeter:
    • 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]
  • Norman Johnson Uniform Polytopes, Manuscript (1991)
    • N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
  • Template:KlitzingPolytopes x3o3o3o4x - scan, x3o3o3x4x - capt, x3o3x3o4x - carnit, x3o3x3x4x - cogrin, x3x3o3x4x - captint, x3x3x3x4x - gacnet, x3x3x3o4x - cogart

Template:Polytopes

  1. ↑ Klitzing, (x3o3o3o4x - scan)
  2. ↑ Klitzing, (x3o3o3x4x - capt)
  3. ↑ Klitzing, (x3o3x3o4x - carnit)
  4. ↑ Klitzing, (x3o3x3x4x - cogrin)
  5. ↑ Klitzing, (x3x3o3x4x - captint)
  6. ↑ Klitzing, (x3x3o3o4x - cappin)
  7. ↑ Klitzing, (x3x3x3o4x - cogart)
  8. ↑ Klitzing, (x3x3x3x4x - gacnet)
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