Dodecahedral truncate (EntityTopic, 11)
From Hi.gher. Space
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| + | <[#ontology [kind topic] [cats 3D Uniform Polytope]]> | ||
{{STS Shape | {{STS Shape | ||
| - | | image= | + | | image=<[#embed [hash 6SYAGTYX8Y54PG89RD7DMZJ1AY] [width 180]]> |
| dim=3 | | dim=3 | ||
| elements=32, 90, 60 | | elements=32, 90, 60 | ||
| + | | sym=[[Rhodohedral symmetry|I<sub>h</sub>, H<sub>3</sub>, [5,3], (*532)]] | ||
| genus=0 | | genus=0 | ||
| ssc={G5<sup>3</sup>}X3 | | ssc={G5<sup>3</sup>}X3 | ||
| - | | extra={{STS Uniform polytope | + | | ssc2=Ki3 |
| + | | extra={{STS Polytope | ||
| + | | flayout={{FLD|a3|i|a5|er}} | ||
| + | | dual=[[Triakis icosahedron]] | ||
| + | | bowers=Ti | ||
| + | }}{{STS Uniform polytope | ||
| schlaefli=t{[[Pentagon|5,]]3} | | schlaefli=t{[[Pentagon|5,]]3} | ||
| + | | conway=t[[Dodecahedron|d]][[Icosahedron|s]][[Tetrahedron|Y3]] | ||
| vfigure=Isosceles [[triangle]] | | vfigure=Isosceles [[triangle]] | ||
| vlayout=[[Triangle|3]]⋅[[Decagon|10]]<sup>2</sup> | | vlayout=[[Triangle|3]]⋅[[Decagon|10]]<sup>2</sup> | ||
| - | |||
| - | |||
| - | |||
}}}} | }}}} | ||
| - | + | <[#polytope [id 22]]> | |
| - | + | {{Trishapes}} | |
Latest revision as of 11:29, 2 March 2014
Incidence matrix
Dual: triakis icosahedron
| # | TXID | Va | Ea | Eb | 10a | 3a | Type | Name |
|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | |||||
| 1 | Ea | 2 | = digon | ; | ||||
| 2 | Eb | 2 | = digon | ; | ||||
| 3 | 10a | 10 | 5 | 5 | = decagon | ; | ||
| 4 | 3a | 3 | 0 | 3 | = triangle | ; | ||
| 5 | C1a | 60 | 30 | 60 | 12 | 20 | = truncated dodecahedron | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
| 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 |
