Stauropantohedron (EntityTopic, 11)
From Hi.gher. Space
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| dim=3 | | dim=3 | ||
| elements=26, 72, 48 | | elements=26, 72, 48 | ||
| + | | sym=[[Staurohedral symmetry|O<sub>h</sub>, BC<sub>3</sub>, [4,3], (*432)]] | ||
| ssc=[xyz]X7 | | ssc=[xyz]X7 | ||
| ssc2=Ko7 | | ssc2=Ko7 | ||
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| altern=[[Snub staurohedron]] | | altern=[[Snub staurohedron]] | ||
| dual=[[Disdyakis dodecahedron]] | | dual=[[Disdyakis dodecahedron]] | ||
| + | | bowers=Girco | ||
}}{{STS Uniform polytope | }}{{STS Uniform polytope | ||
| wythoff=<nowiki>2 3 4 |</nowiki> | | wythoff=<nowiki>2 3 4 |</nowiki> | ||
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| vlayout=[[Square|4]]⋅[[Hexagon|6]]⋅[[Octagon|8]] | | vlayout=[[Square|4]]⋅[[Hexagon|6]]⋅[[Octagon|8]] | ||
| vfigure=[[Triangle]] | | vfigure=[[Triangle]] | ||
| - | |||
}}}} | }}}} | ||
The '''stauropantohedron''', also known as the '''omnitruncated cube''', '''great rhombicuboctahedron''', '''rhombitruncated cuboctahedron''' and '''truncated cuboctahedron''', is the [[omnitruncate]] of the [[cube]] and [[octahedron]]. | The '''stauropantohedron''', also known as the '''omnitruncated cube''', '''great rhombicuboctahedron''', '''rhombitruncated cuboctahedron''' and '''truncated cuboctahedron''', is the [[omnitruncate]] of the [[cube]] and [[octahedron]]. | ||
Latest revision as of 11:15, 2 March 2014
The stauropantohedron, also known as the omnitruncated cube, great rhombicuboctahedron, rhombitruncated cuboctahedron and truncated cuboctahedron, is the omnitruncate of the cube and octahedron.
Incidence matrix
Dual: disdyakis dodecahedron
| # | TXID | Va | Ea | Eb | Ec | 8a | 4a | 6a | Type | Name |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | |||||||
| 1 | Ea | 2 | = digon | ; | ||||||
| 2 | Eb | 2 | = digon | ; | ||||||
| 3 | Ec | 2 | = digon | ; | ||||||
| 4 | 8a | 8 | 4 | 4 | 0 | = octagon | ; | |||
| 5 | 4a | 4 | 2 | 0 | 2 | = square | ; | |||
| 6 | 6a | 6 | 0 | 3 | 3 | = hexagon | ; | |||
| 7 | C1a | 48 | 24 | 24 | 24 | 6 | 12 | 8 | = stauropantohedron | ; |
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 |
