Icosahedron (EntityTopic, 12)
From Hi.gher. Space
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| - | {{Shape|Icosahedron|www.rogersconnection.com | + | {{Shape|Icosahedron|www.rogersconnection.com/icosahedron.jpg |
|3|20, 30, 12|0|{[[Triangle|3,]]5}|<nowiki>5 | 2 3 </nowiki>|''Unknown''|N/A|Regular [[pentagon]], edge 1|Ike|[[Dodecahedron]]}} | |3|20, 30, 12|0|{[[Triangle|3,]]5}|<nowiki>5 | 2 3 </nowiki>|''Unknown''|N/A|Regular [[pentagon]], edge 1|Ike|[[Dodecahedron]]}} | ||
== Geometry == | == Geometry == | ||
Revision as of 17:27, 17 July 2007
Geometry
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 |
