- Snub icosidodecadodecahedron
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Snub icosidodecadodecahedron Type Uniform star 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, [5,3]+, 532 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.
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.
See also
External links
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