Rhodopantohedron (EntityTopic, 11)
From Hi.gher. Space
The rhodopantohedron, also known as the omnitruncated dodecahedron, great rhombicosidodecahedron, rhombitruncated icosidodecahedron and truncated icosidodecahedron, is the omnitruncate of the dodecahedron and icosahedron.
Incidence matrix
Dual: disdyakis triacontahedron
| # | TXID | Va | Ea | Eb | Ec | 10a | 4a | 6a | Type | Name |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | |||||||
| 1 | Ea | 2 | = digon | ; | ||||||
| 2 | Eb | 2 | = digon | ; | ||||||
| 3 | Ec | 2 | = digon | ; | ||||||
| 4 | 10a | 10 | 5 | 5 | 0 | = decagon | ; | |||
| 5 | 4a | 4 | 2 | 0 | 2 | = square | ; | |||
| 6 | 6a | 6 | 0 | 3 | 3 | = hexagon | ; | |||
| 7 | C1a | 120 | 60 | 60 | 60 | 12 | 30 | 20 | = rhodopantohedron | ; |
Usage as facets
- 2× 1-facets of a castellated rhodopantohedral 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 |
