Snub demitesseract (EntityTopic, 11)

From Hi.gher. Space

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It is composed of 120 [[tetrahedra]] and 24 [[icosahedra]]; five tetrahedra and three icosahedra meet at each vertex. In total it has 480 [[triangular]] faces, 432 edges, and 96 vertices.
It is composed of 120 [[tetrahedra]] and 24 [[icosahedra]]; five tetrahedra and three icosahedra meet at each vertex. In total it has 480 [[triangular]] faces, 432 edges, and 96 vertices.
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The [[hydrochoron]] can be constructed by [[kis|raising pyramids on each face]] of the xylochoric snub.
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The [[hydrochoron]] can be constructed by [[kis|raising pyramids on each face]] of the snub demitesseract. Conversely, the snub demitesseract can be constructed by removing the vertices of one of the five inscribed [[xylochora]] from a hydrochoron. Removing the vertices of a second xylochoron yields the [[bixylodiminished hydrochoron]].
{{Tetrashapes}}
{{Tetrashapes}}
[[Category:Uniform polychora]]
[[Category:Uniform polychora]]

Revision as of 23:05, 21 August 2012


The snub demitesseract is the sole uniform snub polychoron form. It can be formed by the construction of alternated truncated 24-cell or alternated cantitruncated 16-cell, and is often called the "snub 24-cell" (equivalently "snub icositetrachoron" and "snub xylochoron"). However, it's not a snub of either family, as the alternation is not of either parent's omnitruncate.

When correctly represented, the snub demitesseract's Coxeter-Dynkin symbol is that of a three-pronged star, with all four nodes as snub rings.

It is composed of 120 tetrahedra and 24 icosahedra; five tetrahedra and three icosahedra meet at each vertex. In total it has 480 triangular faces, 432 edges, and 96 vertices.

The hydrochoron can be constructed by raising pyramids on each face of the snub demitesseract. Conversely, the snub demitesseract can be constructed by removing the vertices of one of the five inscribed xylochora from a hydrochoron. Removing the vertices of a second xylochoron yields the bixylodiminished hydrochoron.


Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonecylindronediconeconinder
Torii: tigertorispherespheritorustorinderditorus