Rectified snub demitesseract (EntityTopic, 13)
From Hi.gher. Space
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| - | The '''rectified snub demitesseract''' is a [[CRF polychoron]] derived from the [[snub demitesseract]] via [[rectification]]. Its surface consists of 24 [[icosidodecahedra]], 96 [[tridiminished icosahedra]], and 120 [[octahedra]] (of two kinds: 96 that share a face with the icosidodecahedra, and 24 that only share faces with octahedra of the first kind). | + | The '''rectified snub demitesseract''' is a [[CRF polychoron]] derived from the [[snub demitesseract]] via [[rectification]]. Its surface consists of 24 [[icosidodecahedra]], 96 [[tridiminished icosahedra]], and 120 [[octahedra]] (of two kinds: 96 that share a face with the icosidodecahedra, and 24 that only share faces with octahedra of the first kind). It was discovered by [[Andrew Weimholt]] in 2004. |
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| + | == Projections == | ||
<[#embed [hash 6C2M2H6DG0NSW40ZK5XAE9GCVC]]> | <[#embed [hash 6C2M2H6DG0NSW40ZK5XAE9GCVC]]> | ||
| + | |||
| + | == Coordinates == | ||
| + | <pre> | ||
| + | apacs<0, 0, 2*phi, 2*phi^2> | ||
| + | apacs<1, 1, phi^3, phi^3> | ||
| + | |||
| + | epacs<0, phi^2, phi^3, 2+phi> | ||
| + | epacs<1, phi, 2*phi^2, phi^2> | ||
| + | </pre> | ||
| + | |||
| + | <[#polytope [id 105]]> | ||
| + | |||
| + | == Software models == | ||
| + | *[[Polyview]] [http://hddb.teamikaria.com/dl/9FC9YAEMKX4JME8P3YX9AZRNKA.def .def file] | ||
| + | *[[Stella4D]] [http://hddb.teamikaria.com/dl/PSX7TFBZ0MYDGMZS711SA9E8H4.off .off file] | ||
Latest revision as of 08:31, 27 March 2014
The rectified snub demitesseract is a CRF polychoron derived from the snub demitesseract via rectification. Its surface consists of 24 icosidodecahedra, 96 tridiminished icosahedra, and 120 octahedra (of two kinds: 96 that share a face with the icosidodecahedra, and 24 that only share faces with octahedra of the first kind). It was discovered by Andrew Weimholt in 2004.
Projections
Coordinates
apacs<0, 0, 2*phi, 2*phi^2> apacs<1, 1, phi^3, phi^3> epacs<0, phi^2, phi^3, 2+phi> epacs<1, phi, 2*phi^2, phi^2>
Incidence matrix
Dual: (dual of rectified snub demitesseract)
| # | TXID | Va | Vb | Ea | Eb | Ec | Ed | 3a | 3b | 3c | 3d | 5a | 3e | 3f | C1a | C2a | C2b | C3a | Type | Name |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; "head" of {5} | |||||||||||||||||
| 1 | Vb | = point | ; "arms" "legs" of {5} | |||||||||||||||||
| 2 | Ea | 2 | 0 | = digon | ; | |||||||||||||||
| 3 | Eb | 1 | 1 | = digon | ; | |||||||||||||||
| 4 | Ec | 0 | 2 | = digon | ; | |||||||||||||||
| 5 | Ed | 0 | 2 | = digon | ; | |||||||||||||||
| 6 | 3a | 3 | 0 | 3 | 0 | 0 | 0 | = triangle | ; | |||||||||||
| 7 | 3b | 3 | 0 | 3 | 0 | 0 | 0 | = triangle | ; | |||||||||||
| 8 | 3c | 1 | 2 | 0 | 2 | 0 | 1 | = triangle | ; | |||||||||||
| 9 | 3d | 2 | 1 | 1 | 2 | 0 | 0 | = triangle | ; | |||||||||||
| 10 | 5a | 1 | 4 | 0 | 2 | 2 | 1 | = pentagon | ; | |||||||||||
| 11 | 3e | 0 | 3 | 0 | 0 | 3 | 0 | = triangle | ; | |||||||||||
| 12 | 3f | 0 | 3 | 0 | 0 | 0 | 3 | = triangle | ; | |||||||||||
| 13 | C1a | 6 | 24 | 0 | 24 | 24 | 12 | 0 | 0 | 12 | 0 | 12 | 8 | 0 | = rhodomesohedron | ; | ||||
| 14 | C2a | 6 | 0 | 12 | 0 | 0 | 0 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | = octahedron | ; tet sym | ||||
| 15 | C2b | 3 | 3 | 3 | 6 | 0 | 3 | 1 | 0 | 3 | 3 | 0 | 0 | 1 | = octahedron | ; 3 ap sym | ||||
| 16 | C3a | 3 | 6 | 3 | 6 | 3 | 3 | 0 | 1 | 0 | 3 | 3 | 0 | 1 | = tridiminished icosahedron | ; | ||||
| 17 | H4.1a | 144 | 288 | 288 | 576 | 288 | 288 | 96 | 96 | 288 | 288 | 288 | 96 | 96 | 24 | 24 | 96 | 96 | = rectified snub demitesseract | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
