Dodecahedron (EntityTopic, 12)
From Hi.gher. Space
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| wythoff=<nowiki>3 | 2 5 </nowiki> | | wythoff=<nowiki>3 | 2 5 </nowiki> | ||
| schlaefli={[[Pentagon|5,]]3} | | schlaefli={[[Pentagon|5,]]3} | ||
| + | | conway=d[[Icosahedron|s]][[Tetrahedron|Y3]] | ||
| vlayout=[[Pentagon|5]]<sup>3</sup> | | vlayout=[[Pentagon|5]]<sup>3</sup> | ||
| vfigure=Equilateral [[triangle]], edge ''tau'' | | vfigure=Equilateral [[triangle]], edge ''tau'' | ||
Revision as of 10:46, 7 November 2008
Equations
- Assumption: Dodecahedron is centered at the origin.
- Variables:
l ⇒ length of edges of the dodecahedron
- The hypervolumes of a dodecahedron are given by:
total edge length = 30l
surface area = 15l2tan(3π10-1)
volume = 5l3(tan(3π10-1))2(tan(sin-1(2sin(π5-1))-1))2-1
- The planar cross-sections (n) of a dodecahedron 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 |
