Icosahedron (EntityTopic, 12)
From Hi.gher. Space
(Difference between revisions)
m |
|||
| Line 6: | Line 6: | ||
| genus=0 | | genus=0 | ||
| ssc={G3<sup>5</sup>} | | ssc={G3<sup>5</sup>} | ||
| + | | ssc2=Ki4 | ||
| pv_circle=~0.6055 | | pv_circle=~0.6055 | ||
| extra={{STS Uniform polytope | | extra={{STS Uniform polytope | ||
Revision as of 17:45, 29 October 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 |
