Tridiminished icosahedron (EntityTopic, 10)
From Hi.gher. Space
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{{STS Shape | {{STS Shape | ||
| name=Tridiminished icosahedron | | name=Tridiminished icosahedron | ||
| + | | image=<[#img [hash BYG0WBQWWCPDRE0BK8YAPNR162] [width 150]]> | ||
| dim=3 | | dim=3 | ||
| - | | elements= | + | | elements=8, 15, 9 |
| genus=0 | | genus=0 | ||
| extra={{STS Polytope | | extra={{STS Polytope | ||
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| - | The '''tridiminished icosahedron''' is the 63rd [[Johnson solid]], J63. It suddenly became important when the [[bixylodiminished hydrochoron]] was discovered. It is the only CRF 3D member of the family of [[ursatope]]s. | + | The '''tridiminished icosahedron''' is the 63rd [[Johnson solid]], J63. It suddenly became important when the [[bixylodiminished hydrochoron]] was discovered. It is the only CRF 3D member of the family of [[ursatope]]s, and appears as cells in the majority of the higher-dimensional ones. |
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| + | == Equations == | ||
| + | *The [[hypervolume]]s of a tridiminished icosahedron with side length ''l'' are given by: | ||
| + | <blockquote>total edge length = 15''l''<br> | ||
| + | surface area = {{Over|1|4}} · (3√(25+10√5) + 5√3) {{DotHV}}<br> | ||
| + | volume = {{Over|(15+7√5)|24}} {{DotHV|3}}</blockquote> | ||
{{Trishapes}} | {{Trishapes}} | ||
Revision as of 18:48, 25 August 2012
The tridiminished icosahedron is the 63rd Johnson solid, J63. It suddenly became important when the bixylodiminished hydrochoron was discovered. It is the only CRF 3D member of the family of ursatopes, and appears as cells in the majority of the higher-dimensional ones.
Equations
- The hypervolumes of a tridiminished icosahedron with side length l are given by:
total edge length = 15l
surface area = 1∕4 · (3√(25+10√5) + 5√3) · l2
volume = (15+7√5)∕24 · l3
| 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 |
