Pyrorectichoron (EntityTopic, 11)
From Hi.gher. Space
(Add Petrie polygon) |
m (Plain image too) |
||
| Line 1: | Line 1: | ||
<[#ontology [kind topic] [cats 4D Uniform Polytope] [alt [[wikipedia:Rectified_5-cell]]]]> | <[#ontology [kind topic] [cats 4D Uniform Polytope] [alt [[wikipedia:Rectified_5-cell]]]]> | ||
{{STS Shape | {{STS Shape | ||
| - | | image=<[#embed [hash | + | | image=<[#embed [hash 8PDKJVVWYTWKJ9MY5T4TAHV0XM] [width 150]]><br/>Petrie polygon |
| dim=4 | | dim=4 | ||
| elements=10, 30, 30, 10 | | elements=10, 30, 30, 10 | ||
Revision as of 14:22, 13 March 2016
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 highlights two neighboring (at a point) tetrahedral cells in red and orange and one octahedral cell in blue:
As there are a total of 5 tetrahedra and 5 octahedra in the figure, 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 |
