Rhodoperihedron (EntityTopic, 11)
From Hi.gher. Space
(Difference between revisions)
(polytope explorer integration) |
m (move Bowers acronym from Template:STS Uniform polytope as it is now being used for non-uniforms too) |
||
| Line 9: | Line 9: | ||
| flayout={{FLD|a3|i|a2|i|a5|cr}} | | flayout={{FLD|a3|i|a2|i|a5|cr}} | ||
| dual=[[Deltoidal hexecontahedron]] | | dual=[[Deltoidal hexecontahedron]] | ||
| + | | bowers=Srid | ||
}}{{STS Uniform polytope | }}{{STS Uniform polytope | ||
| wythoff=<nowiki>3 5 | 2</nowiki> | | wythoff=<nowiki>3 5 | 2</nowiki> | ||
| Line 15: | Line 16: | ||
| 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 [[Tamfang name]]s so that they aren't so ridiculously long). | 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 [[Tamfang name]]s so that they aren't so ridiculously long). | ||
Revision as of 10:29, 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 |
