Snub icosidodecadodecahedron

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(s)	|5/3 3 5
Symmetry group	I, [5,3]+, 532
Index references	U46, C58, W112
Bowers acronym	Sided
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

• List of uniform polyhedra

External links

• Weisstein, Eric W., "Snub icosidodecadodecahedron", MathWorld.