Dodecahedron (EntityTopic, 12)
From Higher Dimensions Database
Equations
- The hypervolumes of a dodecahedron with side length l are given by:
total edge length = 30l
surface area = 3√(25 + 10√5) · l^{2}
volume = ^{(15 + 7√5)}∕_{4} · l^{3}
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 |