Dodecahedron (EntityTopic, 12)
From Hi.gher. Space
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| vfigure=Equilateral [[triangle]], edge ''tau'' | | vfigure=Equilateral [[triangle]], edge ''tau'' | ||
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| dual=[[Icosahedron]] | | dual=[[Icosahedron]] | ||
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Revision as of 10:29, 2 March 2014
Equations
- The hypervolumes of a dodecahedron with side length l are given by:
total edge length = 30l
surface area = 3√(25 + 10√5) · l2
volume = (15 + 7√5)∕4 · l3
Incidence matrix
Dual: icosahedron
| # | TXID | Va | Ea | 5a | Type | Name |
|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | |||
| 1 | Ea | 2 | = digon | ; | ||
| 2 | 5a | 5 | 5 | = pentagon | ; | |
| 3 | C1a | 20 | 30 | 12 | = dodecahedron | ; |
Usage as facets
- 120× 1-facets of a cosmochoron
| 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 |
