# Snub demitesseract (EntityTopic, 11)

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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. | ||

- | The [[hydrochoron]] can be constructed by [[kis|raising pyramids on each | + | The [[hydrochoron]] can be constructed by [[kis|raising pyramids on each icosahedral facet]] 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]]. |

The snub demitesseract can be truncated to form the [[truncated snub demitesseract]], or rectified to form the [[rectified snub demitesseract]], both of which are [[CRF polychora]]. It can also be [[Stott-expanded]] at its icosahedral cells to form the [[runcinated snub demitesseract]], which is [[scaliform]]. | The snub demitesseract can be truncated to form the [[truncated snub demitesseract]], or rectified to form the [[rectified snub demitesseract]], both of which are [[CRF polychora]]. It can also be [[Stott-expanded]] at its icosahedral cells to form the [[runcinated snub demitesseract]], which is [[scaliform]]. | ||

{{Tetrashapes}} | {{Tetrashapes}} |

## Revision as of 18:08, 19 September 2017

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 icosahedral facet 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.

The snub demitesseract can be truncated to form the truncated snub demitesseract, or rectified to form the rectified snub demitesseract, both of which are CRF polychora. It can also be Stott-expanded at its icosahedral cells to form the runcinated snub demitesseract, which is scaliform.

Notable Tetrashapes
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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 |