Icosahedron (EntityTopic, 12)
From Hi.gher. Space
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| - | {{Shape | + | {{STS Shape |
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| name=Icosahedron | | name=Icosahedron | ||
| image=http://fusion-global.org/share/icosahedron.png | | image=http://fusion-global.org/share/icosahedron.png | ||
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| elements=20, 30, 12 | | elements=20, 30, 12 | ||
| genus=0 | | genus=0 | ||
| - | |||
| ssc={G3<sup>5</sup>} | | ssc={G3<sup>5</sup>} | ||
| pv_circle=~0.6055 | | pv_circle=~0.6055 | ||
| + | | extra={{STS Uniform polytope | ||
| wythoff=<nowiki>5 | 2 3 </nowiki> | | wythoff=<nowiki>5 | 2 3 </nowiki> | ||
| schlaefli={[[Triangle|3,]]5} | | schlaefli={[[Triangle|3,]]5} | ||
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| kana=ｲｺ | | kana=ｲｺ | ||
| dual=[[Dodecahedron]] | | dual=[[Dodecahedron]] | ||
| - | }} | + | }}}} |
| + | |||
== Equations == | == Equations == | ||
*Assumption: Icosahedron is centered at the origin. | *Assumption: Icosahedron is centered at the origin. | ||
Revision as of 15:13, 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 |
