Rhodopantohedron (EntityTopic, 11)
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| + | <[#ontology [kind topic] [cats 3D Uniform Polytope]]> | ||
{{STS Shape | {{STS Shape | ||
| dim=3 | | dim=3 | ||
| elements=62, 180, 120 | | elements=62, 180, 120 | ||
| + | | sym=[[Rhodohedral symmetry|I<sub>h</sub>, H<sub>3</sub>, [5,3], (*532)]] | ||
| ssc={G5<sup>3</sup>}X7 | | ssc={G5<sup>3</sup>}X7 | ||
| ssc2=Ki7 | | ssc2=Ki7 | ||
| extra={{STS Polytope | | extra={{STS Polytope | ||
| - | | flayout={{FLD| | + | | flayout={{FLD|a2tr|ti|a3tm|ti|a5tl|cr}} |
| - | | altern=[[Snub | + | | altern=[[Snub rhodohedron]] |
| dual=[[Disdyakis triacontahedron]] | | dual=[[Disdyakis triacontahedron]] | ||
| + | | bowers=Grid | ||
}}{{STS Uniform polytope | }}{{STS Uniform polytope | ||
| wythoff=<nowiki>2 3 5 |</nowiki> | | wythoff=<nowiki>2 3 5 |</nowiki> | ||
| schlaefli=ot{5,3} or ot{3,5} | | schlaefli=ot{5,3} or ot{3,5} | ||
| - | | conway=t | + | | conway=t[[Icosidodecahedron|a]][[Icosahedron|s]][[Tetrahedron|Y3]] |
| vlayout=[[Square|4]]⋅[[Hexagon|6]]⋅[[Decagon|10]] | | vlayout=[[Square|4]]⋅[[Hexagon|6]]⋅[[Decagon|10]] | ||
| vfigure=[[Triangle]] | | vfigure=[[Triangle]] | ||
| - | |||
| - | |||
}}}} | }}}} | ||
| + | The '''rhodopantohedron''', also known as the '''omnitruncated dodecahedron''', '''great rhombicosidodecahedron''', '''rhombitruncated icosidodecahedron''' and '''truncated icosidodecahedron''', is the [[omnitruncate]] of the [[dodecahedron]] and [[icosahedron]]. | ||
| - | + | <[#polytope [id 28]]> | |
| - | + | {{Trishapes}} | |
Latest revision as of 11:29, 2 March 2014
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 |
