Rhodoperihedron (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=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 | ||
| - | | extra={{STS Uniform polytope | + | | ssc2=Ki5 |
| + | | extra={{STS Polytope | ||
| + | | flayout={{FLD|a3|i|a2|i|a5|cr}} | ||
| + | | dual=[[Deltoidal hexecontahedron]] | ||
| + | | bowers=Srid | ||
| + | }}{{STS Uniform polytope | ||
| wythoff=<nowiki>3 5 | 2</nowiki> | | wythoff=<nowiki>3 5 | 2</nowiki> | ||
| schlaefli=rr{5,3} or rr{3,5} | | schlaefli=rr{5,3} or rr{3,5} | ||
| + | | conway=a[[Icosidodecahedron|a]][[Icosahedron|s]][[Tetrahedron|Y3]] | ||
| vlayout=[[Triangle|3]]⋅[[Square|4]]⋅[[Pentagon|5]]⋅[[Square|4]] | | vlayout=[[Triangle|3]]⋅[[Square|4]]⋅[[Pentagon|5]]⋅[[Square|4]] | ||
| vfigure=[[Trapezium]], sides {1, √2, φ, √2} | | vfigure=[[Trapezium]], sides {1, √2, φ, √2} | ||
| - | |||
| - | |||
| - | |||
}}}} | }}}} | ||
| + | The '''rhodoperihedron''', also known as the '''(small) rhombicosidodecahedron''', is the [[peritruncate]] of the [[dodecahedron]] and [[icosahedron]]. There are 12 [[Johnson solids]], J<sub>72</sub> to J<sub>83</sub>, which are named after this shape (hence the push for [[elemental name]]s so that they aren't so ridiculously long). | ||
| - | + | <[#polytope [id 26]]> | |
| - | + | {{Trishapes}} | |
Latest revision as of 14:07, 15 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 elemental 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 |
