Cubic truncate (EntityTopic, 11)
From Hi.gher. Space
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The '''cubic truncate''' ('''CT''') is a uniform polyhedron which can be seen as a 3-dimensional analog of the [[octagon]]. The other possible analog is the [[cuboctahedral rectate]] (''COR''). While the CT has the octagons on the surface of the shape, the COR has them embedded inside it. Thus when one is concerned with [[powertopes]], the COR comprises three "long and thin" cuboids whereas the CT comprises three "wide and flat" cuboids. | The '''cubic truncate''' ('''CT''') is a uniform polyhedron which can be seen as a 3-dimensional analog of the [[octagon]]. The other possible analog is the [[cuboctahedral rectate]] (''COR''). While the CT has the octagons on the surface of the shape, the COR has them embedded inside it. Thus when one is concerned with [[powertopes]], the COR comprises three "long and thin" cuboids whereas the CT comprises three "wide and flat" cuboids. | ||
Revision as of 10:34, 2 March 2014
The cubic truncate (CT) is a uniform polyhedron which can be seen as a 3-dimensional analog of the octagon. The other possible analog is the cuboctahedral rectate (COR). While the CT has the octagons on the surface of the shape, the COR has them embedded inside it. Thus when one is concerned with powertopes, the COR comprises three "long and thin" cuboids whereas the CT comprises three "wide and flat" cuboids.
Incidence matrix
Dual: triakis octahedron
| # | TXID | Va | Ea | Eb | 8a | 3a | Type | Name |
|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | |||||
| 1 | Ea | 2 | = digon | ; | ||||
| 2 | Eb | 2 | = digon | ; | ||||
| 3 | 8a | 8 | 4 | 4 | = octagon | ; | ||
| 4 | 3a | 3 | 0 | 3 | = triangle | ; | ||
| 5 | C1a | 24 | 12 | 24 | 6 | 8 | = truncated cube | ; |
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 |
