Great snub icosidodecahedron
From Wikipedia, the free encyclopedia
| Great snub icosidodecahedron | |
|---|---|
 |
|
| Type | Uniform polyhedron |
| Elements | F = 92, E = 150 V = 60 (χ = 2) |
| Faces by sides | (20+60){3}+12{5/2} |
| Wythoff symbol | |2 5/2 3 |
| Symmetry group | I |
| Index references | U57, C88, W116 |
 34.5/2 (Vertex figure) |
 Great pentagonal hexecontahedron (dual polyhedron) |
In geometry, the great snub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U57.
This polyhedron can be considered a snub great icosahedron.
[edit] Cartesian coordinates
Cartesian coordinates for the vertices of a great snub icosidodecahedron are all the even permutations of
- (±2α, ±2, ±2β),
- (±(α−βτ−1/τ), ±(α/τ+β−τ), ±(−ατ−β/τ−1)),
- (±(ατ−β/τ+1), ±(−α−βτ+1/τ), ±(−α/τ+β+τ)),
- (±(ατ−β/τ−1), ±(α+βτ+1/τ), ±(−α/τ+β−τ)) and
- (±(α−βτ+1/τ), ±(−α/τ−β−τ), ±(−ατ−β/τ+1)),
with an even number of plus signs, where
- α = ξ−1/ξ
and
- β = −ξ/τ+1/τ2−1/(ξτ),
where τ = (1+√5)/2 is the golden mean and ξ is the negative real solution to ξ3−2ξ=−1/τ, or approximately −1.5488772. Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one.
