Icosahedron (EntityTopic, 12)
From Hi.gher. Space
(Difference between revisions)
m |
m |
||
| Line 8: | Line 8: | ||
| ssc2=Ki4 | | ssc2=Ki4 | ||
| pv_circle=~0.6055 | | pv_circle=~0.6055 | ||
| - | | extra={{STS Uniform polytope | + | | extra={{STS Polytope |
| + | | flayout={{FLD|a3|end|e5}} | ||
| + | | petrie=10,2 | ||
| + | | dual=[[Dodecahedron]] | ||
| + | }}{{STS Uniform polytope | ||
| wythoff=<nowiki>5 | 2 3 </nowiki> | | wythoff=<nowiki>5 | 2 3 </nowiki> | ||
| schlaefli={[[Triangle|3,]]5} | | schlaefli={[[Triangle|3,]]5} | ||
| Line 16: | Line 20: | ||
| bowers=Ike | | bowers=Ike | ||
| kana=ｲｺ | | kana=ｲｺ | ||
| - | |||
}}}} | }}}} | ||
Revision as of 11:04, 1 November 2009
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 |
