Pyrorectichoron (EntityTopic, 11)

From Hi.gher. Space

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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 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.
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<[#polytope [id 128]]>
{{Tetrashapes}}
{{Tetrashapes}}

Revision as of 13:37, 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.

Incidence matrix

Dual: (dual of pyrorectichoron)

#TXIDVaEa3a3bC1aC2aTypeName
0 Va = point ;
1 Ea 2 = digon ;
2 3a 33 = triangle ; tet-oct
3 3b 33 = triangle ; oct-oct
4 C1a 4640 = tetrahedron ;
5 C2a 61244 = octahedron ;
6 H4.1a 1030201055 = pyrorectichoron ;

Usage as facets

This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.


Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonecylindronediconeconinder
Torii: tigertorispherespheritorustorinderditorus