Snub icosidodecadodecahedron
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| Snub icosidodecadodecahedron | |
|---|---|
 |
|
| Type | Uniform polyhedron |
| Elements | F = 104, E = 180 V = 60 (χ = -16) |
| Faces by sides | (20+60){3}+12{5}+12{5/2} |
| Wythoff symbol | |5/3 3 5 |
| Symmetry group | I |
| Index references | U46, C58, W112 |
 3.3.3.5.3.5/3 (Vertex figure) |
 Medial hexagonal hexecontahedron (dual polyhedron) |
In geometry, the snub icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U46.
[edit] Cartesian coordinates
Cartesian coordinates for the vertices of a snub icosidodecadodecahedron are all the even permutations of
- (±2α, ±2γ, ±2β),
- (±(α+β/τ+γτ), ±(-ατ+β+γ/τ), ±(α/τ+βτ-γ)),
- (±(-α/τ+βτ+γ), ±(-α+β/τ-γτ), ±(ατ+β-γ/τ)),
- (±(-α/τ+βτ-γ), ±(α-β/τ-γτ), ±(ατ+β+γ/τ)) and
- (±(α+β/τ-γτ), ±(ατ-β+γ/τ), ±(α/τ+βτ+γ)),
with an even number of plus signs, where
- α = ρ+1,
- β = τ2ρ2+τ2ρ+τ,
- γ = ρ2+τρ,
and where τ = (1+√5)/2 is the golden mean and ρ is the real solution to ρ3=ρ+1, or approximately 1.3247180. ρ is called the plastic constant. Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one.
