Rhodomesohedron (EntityTopic, 11)
From Hi.gher. Space
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| + | <[#ontology [kind topic] [cats 3D Uniform Polytope]]> | ||
{{STS Shape | {{STS Shape | ||
| 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 | ||
| - | | extra={{STS Uniform polytope | + | | ssc2=Ki2 |
| + | | extra={{STS Polytope | ||
| + | | flayout={{FLD|a3|i|a5|cr}} | ||
| + | | dual=[[Rhombic triacontahedron]] | ||
| + | | bowers=Id | ||
| + | }}{{STS Uniform polytope | ||
| wythoff=<nowiki>2 | 3 5</nowiki> | | wythoff=<nowiki>2 | 3 5</nowiki> | ||
| schlaefli=r{[[Pentagon|5]],[[Dodecahedron|3]]} or r{[[Triangle|3]],[[Icosahedron|5]]} | | schlaefli=r{[[Pentagon|5]],[[Dodecahedron|3]]} or r{[[Triangle|3]],[[Icosahedron|5]]} | ||
| + | | conway=a[[Icosahedron|s]][[Tetrahedron|Y3]] | ||
| 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 | ||
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| - | |||
| - | |||
}}}} | }}}} | ||
| + | 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). | ||
| - | + | <[#polytope [id 20]]> | |
{{Trishapes}} | {{Trishapes}} | ||
| - | |||
| - | |||
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 |
