Dodecahedron (EntityTopic, 12)
From Hi.gher. Space
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| - | <[#ontology [kind topic] [cats 3D Regular Polytope]]> | + | <[#ontology [kind topic] [cats 3D Regular Polytope] [alt [[freebase:02bls]] [[wikipedia:Dodecahedron]]]]> |
{{STS Shape | {{STS Shape | ||
| name=Dodecahedron | | name=Dodecahedron | ||
Revision as of 22:57, 3 January 2012
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 = 3√(25 + 10√5) · l2
volume = (15 + 7√5)∕4 · l3
- 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 |
