Icosahedron (EntityTopic, 12)
From Hi.gher. Space
(Difference between revisions)
m (move Bowers acronym from Template:STS Uniform polytope as it is now being used for non-uniforms too) |
(add symmetry group) |
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Line 5: | Line 5: | ||
| dim=3 | | dim=3 | ||
| elements=20, 30, 12 | | elements=20, 30, 12 | ||
+ | | sym=[[Rhodohedral symmetry|I<sub>h</sub>, H<sub>3</sub>, [5,3], (*532)]] | ||
| genus=0 | | genus=0 | ||
| ssc={G3<sup>5</sup>} | | ssc={G3<sup>5</sup>} |
Revision as of 11:00, 2 March 2014
Equations
- The hypervolumes of an icosahedron with side length l are given by:
total edge length = 30l
surface area = 5√3 · l2
volume = 5(3+√5)∕12 · l3
Incidence matrix
Dual: dodecahedron
# | TXID | Va | Ea | 3a | Type | Name |
---|---|---|---|---|---|---|
0 | Va | = point | ; | |||
1 | Ea | 2 | = digon | ; | ||
2 | 3a | 3 | 3 | = triangle | ; | |
3 | C1a | 12 | 30 | 20 | = icosahedron | ; |
Usage as facets
- 6× 1-facets of a tetraaugmented triangular hebesphenorotundaeic rhombochoron
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 |