Pyrorectichoron (EntityTopic, 11)
From Hi.gher. Space
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.
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.
|2||3a||3||3||= triangle||; tet-oct|
|3||3b||3||3||= triangle||; oct-oct|
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
|Regular:||pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron|
|Powertopes:||triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate|
|Circular:||glome • cubinder • duocylinder • spherinder • sphone • dicone • coninder|
|Torii:||tiger • torisphere • spheritorus • torinder • ditorus|