Rhodomesohedron (EntityTopic, 11)
From Hi.gher. Space
(Difference between revisions)
(polytope explorer integration) |
m (add symmetry group) |
||
| (One intermediate revision not shown) | |||
| Line 3: | Line 3: | ||
| dim=3 | | dim=3 | ||
| elements=32, 60, 30 | | elements=32, 60, 30 | ||
| + | | sym=[[Rhodohedral symmetry|I<sub>h</sub>, H<sub>3</sub>, [5,3], (*532)]] | ||
| genus=0 | | genus=0 | ||
| ssc2=Ki2 | | ssc2=Ki2 | ||
| Line 8: | Line 9: | ||
| flayout={{FLD|a3|i|a5|cr}} | | flayout={{FLD|a3|i|a5|cr}} | ||
| dual=[[Rhombic triacontahedron]] | | dual=[[Rhombic triacontahedron]] | ||
| + | | bowers=Id | ||
}}{{STS Uniform polytope | }}{{STS Uniform polytope | ||
| wythoff=<nowiki>2 | 3 5</nowiki> | | wythoff=<nowiki>2 | 3 5</nowiki> | ||
| Line 14: | Line 16: | ||
| vlayout={[[Triangle|3]]⋅[[Pentagon|5]]}<sup>2</sup> | | vlayout={[[Triangle|3]]⋅[[Pentagon|5]]}<sup>2</sup> | ||
| vfigure=[[Rectangle]], edges 1 and φ | | vfigure=[[Rectangle]], edges 1 and φ | ||
| - | |||
}}}} | }}}} | ||
The '''rhodomesohedron''' is the [[mesotruncate]] of the [[dodecahedron]] and [[icosahedron]]. It is also called the '''icosidodecahedron''', which is an interesting name as it represents both the number of faces in the polyhedron ('''icosidodeca''' = 32) and also the combination of the two [[regular polytope]]s that can be [[rectified]] to form it ('''icosa'''hedron + '''dodeca'''hedron). | The '''rhodomesohedron''' is the [[mesotruncate]] of the [[dodecahedron]] and [[icosahedron]]. It is also called the '''icosidodecahedron''', which is an interesting name as it represents both the number of faces in the polyhedron ('''icosidodeca''' = 32) and also the combination of the two [[regular polytope]]s that can be [[rectified]] to form it ('''icosa'''hedron + '''dodeca'''hedron). | ||
Latest revision as of 11:29, 2 March 2014
The rhodomesohedron is the mesotruncate of the dodecahedron and icosahedron. It is also called the icosidodecahedron, which is an interesting name as it represents both the number of faces in the polyhedron (icosidodeca = 32) and also the combination of the two regular polytopes that can be rectified to form it (icosahedron + dodecahedron).
Incidence matrix
Dual: rhombic triacontahedron
| # | TXID | Va | Ea | 3a | 5a | Type | Name |
|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | ||||
| 1 | Ea | 2 | = digon | ; | |||
| 2 | 3a | 3 | 3 | = triangle | ; | ||
| 3 | 5a | 5 | 5 | = pentagon | ; | ||
| 4 | C1a | 30 | 60 | 20 | 12 | = rhodomesohedron | ; |
Usage as facets
- 24× 1-facets of a rectified snub demitesseract
- 1× 1-facets of a D4.7
| 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 |
