Truncated great icosahedron
From Wikipedia, the free encyclopedia
| Truncated great icosahedron | |
|---|---|
 |
|
| Type | Uniform polyhedron |
| Elements | F = 32, E = 90 V = 60 (χ = 2) |
| Faces by sides | 12{5/2}+20{6} |
| Wythoff symbol | 25/2 | 3 |
| Symmetry group | Ih |
| Index references | U55, C71, W95 |
 6.6.5/2 (Vertex figure) |
 Great stellapentakis dodecahedron (dual polyhedron) |
In geometry, the truncated great icosahedron is a nonconvex uniform polyhedron, indexed as U55.
This polyhedron is the truncation of the great icosahedron.
[edit] Cartesian coordinates
Cartesian coordinates for the vertices of a truncated great icosahedron centered at the origin are all the even permutations of
- (±1, 0, ±3/τ)
- (±2, ±1/τ, ±1/τ3)
- (±(1+1/τ2), ±1, ±2/τ)
where τ = (1+√5)/2 is the golden ratio (sometimes written φ). Using 1/τ2 = 1 − 1/τ one verifies that all vertices are on a sphere, centered at the origin, with the radius squared equal to 10−9/τ. The edges have length 2.
