Icosahedron (EntityTopic, 12)
From Hi.gher. Space
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== Equations == | == Equations == | ||
*The [[hypervolume]]s of an icosahedron with side length ''l'' are given by: | *The [[hypervolume]]s of an icosahedron with side length ''l'' are given by: | ||
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surface area = 5√3 {{DotHV}}<br> | surface area = 5√3 {{DotHV}}<br> | ||
volume = {{Over|5(3+√5)|12}} {{DotHV|3}}</blockquote> | volume = {{Over|5(3+√5)|12}} {{DotHV|3}}</blockquote> | ||
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+ | <[#polytope [id 5]]> | ||
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{{Trishapes}} | {{Trishapes}} |
Revision as of 22:09, 16 February 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 |