Icosahedral truncate (EntityTopic, 11)
From Hi.gher. Space
Equations
- Variables:
l ⇒ length of edges of the truncated icosahedron
- The hypervolumes of a truncated icosahedron are given by:
total edge length = 90l
surface area = 3(3^{2-1}10+5^{2-1}(5+5^{2-1}2)^{2-1})l^{2}
volume = (125+5^{2-1}43)l^{3}4^{-1}
Incidence matrix
Dual: pentakis dodecahedron
# | TXID | Va | Ea | Eb | 5a | 6a | Type | Name |
---|---|---|---|---|---|---|---|---|
0 | Va | = point | ; | |||||
1 | Ea | 2 | = digon | ; | ||||
2 | Eb | 2 | = digon | ; | ||||
3 | 5a | 5 | 0 | 5 | = pentagon | ; | ||
4 | 6a | 6 | 3 | 3 | = hexagon | ; | ||
5 | C1a | 60 | 30 | 60 | 12 | 20 | = truncated icosahedron | ; |
Usage as facets
- 24× 1-facets of a truncated snub demitesseract
- 1× 1-facets of a D4.7
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 |