Icosahedron (EntityTopic, 12)
From Hi.gher. Space
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{{STS Shape | {{STS Shape | ||
| name=Icosahedron | | name=Icosahedron | ||
| - | | image=http:// | + | | image=http://teamikaria.com/share/?caption=icosahedron.png |
| dim=3 | | dim=3 | ||
| elements=20, 30, 12 | | elements=20, 30, 12 | ||
Revision as of 19:08, 14 March 2008
Equations
- Assumption: Icosahedron is centered at the origin.
- Variables:
l ⇒ length of edges of the icosahedron
- The hypervolumes of an icosahedron are given by:
total edge length = 30l
surface area = 5sqrt(3)l2
volume = 5l3(3+sqrt(5))12-1
- The planar cross-sections (n) of an icosahedron are:
Unknown
| 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 |
