Pyrorectichoron (EntityTopic, 11)
From Hi.gher. Space
The pyrorectichoron is a uniform polychoron in the pyrotope family. Its cells are 5 tetrahedra and 5 octahedra.
The pyrorectichoron can be constructed as tetrahedron || octahedron, meaning it's also a segmentochoron, K4.5. Deleting any vertex from the pyrorectichoron forms the trigonal biantiprismatic ring, or K4.6, which can be constructed as trigonal prism || gyrated triangle. Deleting another vertex - specifically, one of the three from the gyrated triangle - will form the digonal gyrobicupolic ring, or K4.8.
Images
The following Petrie polygon and stereographic projection each highlight the same arrangement of two neighboring (at a point) tetrahedral cells in red and orange and the octahedral cell between them in blue:
In the Petrie polygon, as there are a total of 5 tetrahedra and 5 octahedra, the others can be obtained by rotating the above highlights by τ∕5.
Incidence matrix
Dual: (dual of pyrorectichoron)
# | TXID | Va | Ea | 3a | 3b | C1a | C2a | Type | Name |
---|---|---|---|---|---|---|---|---|---|
0 | Va | = point | ; | ||||||
1 | Ea | 2 | = digon | ; | |||||
2 | 3a | 3 | 3 | = triangle | ; tet-oct | ||||
3 | 3b | 3 | 3 | = triangle | ; oct-oct | ||||
4 | C1a | 4 | 6 | 4 | 0 | = tetrahedron | ; | ||
5 | C2a | 6 | 12 | 4 | 4 | = octahedron | ; | ||
6 | H4.1a | 10 | 30 | 20 | 10 | 5 | 5 | = pyrorectichoron | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
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 |