Octahedral truncate (EntityTopic, 11)
From Hi.gher. Space
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| + | <[#ontology [kind topic] [cats 3D Uniform Polytope]]> | ||
{{STS Shape | {{STS Shape | ||
| - | | image= | + | | image=<[#embed [hash QTT3C87E6AJ06HAKMKJFRNB07D] [width 180]]> |
| dim=3 | | dim=3 | ||
| elements=14, 36, 24 | | elements=14, 36, 24 | ||
| + | | sym=[[Staurohedral symmetry|O<sub>h</sub>, BC<sub>3</sub>, [4,3], (*432)]] | ||
| genus=0 | | genus=0 | ||
| ssc=[xyz]X6 | | ssc=[xyz]X6 | ||
| - | | extra={{STS Uniform polytope | + | | ssc2=Ko6 |
| + | | extra={{STS Polytope | ||
| + | | flayout={{FLD|a4|i|a3|er}} | ||
| + | | altern=[[Icosahedron]] | ||
| + | | dual=[[Tetrakis hexahedron]] | ||
| + | | bowers=Toe | ||
| + | }}{{STS Uniform polytope | ||
| wythoff=<nowiki>3 | 2 3 or | 2 2 2</nowiki> | | wythoff=<nowiki>3 | 2 3 or | 2 2 2</nowiki> | ||
| schlaefli=t{[[Triangle|3,]][[Octahedron|4]]} | | schlaefli=t{[[Triangle|3,]][[Octahedron|4]]} | ||
| + | | conway=t[[Octahedron|a]][[Tetrahedron|Y3]] | ||
| vfigure=Isosceles [[triangle]] | | vfigure=Isosceles [[triangle]] | ||
| vlayout=[[Square|4]]∙[[Hexagon|6]]<sup>2</sup> | | vlayout=[[Square|4]]∙[[Hexagon|6]]<sup>2</sup> | ||
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| - | |||
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}}}} | }}}} | ||
| + | The '''octahedral truncate''' is a particular uniform polyhedron. It is special because it is one of only five regular-faced convex polyhedra that can tile the realm (the others being the [[cube]], [[triangular prism]], [[hexagonal prism]] and [[gyrobifastigium]]). | ||
| - | + | <[#polytope [id 12]]> | |
| - | + | {{Trishapes}} | |
Latest revision as of 11:13, 2 March 2014
The octahedral truncate is a particular uniform polyhedron. It is special because it is one of only five regular-faced convex polyhedra that can tile the realm (the others being the cube, triangular prism, hexagonal prism and gyrobifastigium).
Incidence matrix
Dual: tetrakis hexahedron
| # | TXID | Va | Ea | Eb | 4a | 6a | Type | Name |
|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | |||||
| 1 | Ea | 2 | = digon | ; | ||||
| 2 | Eb | 2 | = digon | ; | ||||
| 3 | 4a | 4 | 0 | 4 | = square | ; | ||
| 4 | 6a | 6 | 3 | 3 | = hexagon | ; | ||
| 5 | C1a | 24 | 12 | 24 | 6 | 8 | = truncated octahedron | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
| Notable Trishapes | |
| Regular: | tetrahedron • cube • octahedron • dodecahedron • icosahedron |
| Direct truncates: | tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate |
| Mesotruncates: | stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron |
| Snubs: | snub staurohedron • snub rhodohedron |
| Curved: | sphere • torus • cylinder • cone • frustum • crind |
