Rhodoperihedron (EntityTopic, 11)
From Hi.gher. Space
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m (move Bowers acronym from Template:STS Uniform polytope as it is now being used for non-uniforms too) |
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| dim=3 | | dim=3 | ||
| elements=62, 120, 60 | | elements=62, 120, 60 | ||
| + | | sym=[[Rhodohedral symmetry|I<sub>h</sub>, H<sub>3</sub>, [5,3], (*532)]] | ||
| genus=0 | | genus=0 | ||
| ssc={G5<sup>3</sup>}X5 | | ssc={G5<sup>3</sup>}X5 | ||
Revision as of 11:29, 2 March 2014
The rhodoperihedron, also known as the (small) rhombicosidodecahedron, is the peritruncate of the dodecahedron and icosahedron. There are 12 Johnson solids, J72 to J83, which are named after this shape (hence the push for Tamfang names so that they aren't so ridiculously long).
Incidence matrix
Dual: deltoidal hexecontahedron
| # | TXID | Va | Ea | Eb | 5a | 4a | 3a | Type | Name |
|---|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | ||||||
| 1 | Ea | 2 | = digon | ; | |||||
| 2 | Eb | 2 | = digon | ; | |||||
| 3 | 5a | 5 | 5 | 0 | = pentagon | ; | |||
| 4 | 4a | 4 | 2 | 2 | = square | ; | |||
| 5 | 3a | 3 | 0 | 3 | = triangle | ; | |||
| 6 | C1a | 60 | 60 | 60 | 12 | 30 | 20 | = rhodoperihedron | ; |
Usage as facets
- 2× 1-facets of a castellated rhodoperihedral prism
| 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 |
