Snub demitesseract (EntityTopic, 11)
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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. | 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. | ||
Revision as of 10:29, 2 March 2014
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: | pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron |
| Powertopes: | triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate |
| Circular: | glome • cubinder • duocylinder • spherinder • sphone • cylindrone • dicone • coninder |
| Torii: | tiger • torisphere • spheritorus • torinder • ditorus |
