en>NAshbery: /* Determining the probability function */

2012-12-10T21:14:33Z

Determining the probability function

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	~~27 yr old Mechanical Executive Draftsperson Bernard from Val~~-~~Belair~~, ~~has interests including crafts~~ (~~unspecified~~), ~~como~~ [http://~~ganhedinheiro~~.~~comoganhardinheiro101~~.com/ ~~ganhar dinheiro~~] ~~na internet~~ and ~~calligraphy~~. ~~Discovers the beauty in visiting destinations around the world~~, ~~recently only returning from City~~ of ~~Vicenza~~ and ~~the Palladian Villas of the Veneto~~.		{\| class="wikitable" align="right" style="margin-left:10px" width="320"
			!bgcolor=#e7dcc3 colspan=2\|Truncated 4-simplex honeycomb
			\|-
			\|bgcolor=#ffffff align=center colspan=2\|(No image)
			\|-
			\|bgcolor=#e7dcc3\|Type\|\|[[Uniform_polyteron#Regular_and_uniform_honeycombs\|Uniform 4-honeycomb]]
			\|-
			\|bgcolor=#e7dcc3\|Family\|\|[[Truncated simplectic honeycomb]]
			\|-
			\|bgcolor=#e7dcc3\|[[Schläfli symbol]]\|\|t<sub>0,1</sub>{3<sup>[5]</sup>}
			\|-
			\|bgcolor=#e7dcc3\|[[Coxeter diagram]]\|\|{{CDD\|branch_11\|3ab\|nodes\|split2\|node}}
			\|-
			\|bgcolor=#e7dcc3\|4-face types\|\|[[5-cell\|{3,3,3}]] [[File:Schlegel wireframe 5-cell.png\|40px]]<BR>[[Truncated 5-cell\|t{3,3,3}]] [[File:Schlegel half-solid truncated pentachoron.png\|40px]]<BR>[[Bitruncated 5-cell\|2t{3,3,3}]] [[File:Schlegel half-solid bitruncated 5-cell.png\|40px]]
			\|-
			\|bgcolor=#e7dcc3\|Cell types\|\|[[tetrahedron\|{3,3}]] [[File:Tetrahedron.png\|20px]]<BR>[[Truncated tetrahedron\|t{3,3}]] [[File:Truncated tetrahedron.png\|20px]]
			\|-
			\|bgcolor=#e7dcc3\|Face types\|\|[[Triangle]] {3}<BR>[[Hexagon]] {6}
			\|-
			\|bgcolor=#e7dcc3\|Vertex figure\|\|[[File:Truncated_5-cell_honeycomb_verf.png\|100px]]<BR>Elongated [[tetrahedral antiprism]]<BR>[3,4,2<sup>+</sup>], order 48
			\|-
			\|bgcolor=#e7dcc3\|[[Coxeter notation\|Symmetry]]\|\|<math>{\tilde{A}}_4</math>×2, [<span/>[3<sup>[5]</sup>]]
			\|-
			\|bgcolor=#e7dcc3\|Properties\|\|[[vertex-transitive]]
			\|}

			In [[Four-dimensional space\|four-dimensional]] [[Euclidean geometry]], the '''truncated 4-simplex honeycomb''', '''truncated 5-cell honeycomb''' is a space-filling [[tessellation]] [[honeycomb (geometry)\|honeycomb]]. It is composed of [[5-cell]]s, [[truncated 5-cell]]s, and [[bitruncated 5-cell]]s facets in a ratio of 2:2:1. Its [[vertex figure]] is an Elongated [[tetrahedral antiprism]], with 8 [[equilateral triangle]] and 24 [[isosceles triangle]] faces, defining 8 [[5-cell]] and 24 [[truncated 5-cell]] facets around a vertex.

			It can be constructed as five sets of parallel [[hyperplane]]s that divide space into two half-spaces. The 3-space hyperplanes contain [[quarter cubic honeycomb]]s as a collection facets.<ref name=tetra>Olshevsky, 2006 (Model 135)</ref>

			== Alternate names==
			* Cyclotruncated pentachoric tetracomb
			* Small truncated-pentachoric tetracomb

			== Related polytopes and honeycombs ==
			{{A4 honeycombs}}

			==See also==
			Regular and uniform honeycombs in 4-space:
			*[[Tesseractic honeycomb]]
			*[[16-cell honeycomb]]
			*[[24-cell honeycomb]]
			*[[Truncated 24-cell honeycomb]]
			*[[Snub 24-cell honeycomb]]
			*[[5-cell honeycomb]]
			*[[Omnitruncated 5-cell honeycomb]]

			==Notes==
			{{reflist}}

			== References ==
			* [[Norman Johnson (mathematician)\|Norman Johnson]] ''Uniform Polytopes'', Manuscript (1991)
			* '''Kaleidoscopes: Selected Writings of H.S.M. Coxeter''', edited 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] (1.9 Uniform space-fillings)
			** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]
			* [[George Olshevsky]], ''Uniform Panoploid Tetracombs'', Manuscript (2006) ''(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)'' Model 135
			* {{KlitzingPolytopes\|flat.htm\|4D\|Euclidean tesselations}}, x3x3x3x3x3*a - otcypit - 135
			{{Honeycombs}}
			[[Category:Honeycombs (geometry)]]
			[[Category:5-polytopes]]

en>BattyBot: General fixes, removed orphan tag using AWB (8062)

2012-06-27T04:43:19Z

General fixes, removed orphan tag using AWB (8062)

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27 yr old Mechanical Executive Draftsperson Bernard from Val-Belair, has interests including crafts (unspecified), como [http://ganhedinheiro.comoganhardinheiro101.com/ ganhar dinheiro] na internet and calligraphy. Discovers the beauty in visiting destinations around the world, recently only returning from City of Vicenza and the Palladian Villas of the Veneto.

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en>NAshbery: /* Determining the probability function */

en>BattyBot: General fixes, removed orphan tag using AWB (8062)