Icosahedral truncate (EntityTopic, 11)
From Hi.gher. Space
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| extra={{STS Uniform polytope | | extra={{STS Uniform polytope | ||
| schlaefli=t{[[Pentagon|3,]]5} | | schlaefli=t{[[Pentagon|3,]]5} | ||
| + | | conway=t[[Icosahedron|s]][[Tetrahedron|Y3]] | ||
| vfigure=Isosceles [[triangle]] | | vfigure=Isosceles [[triangle]] | ||
| vlayout=[[Pentagon|5]]⋅[[Hexagon|6]]<sup>2</sup> | | vlayout=[[Pentagon|5]]⋅[[Hexagon|6]]<sup>2</sup> | ||
Revision as of 10:47, 7 November 2008
Geometry
Equations
- Variables:
l ⇒ length of edges of the truncated icosahedron
- The hypervolumes of a truncated icosahedron are given by:
total edge length = 90l
surface area = 3(32-110+52-1(5+52-12)2-1)l2
volume = (125+52-143)l34-1
| 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 |
