Small retrosnub icosicosidodecahedron

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Small retrosnub icosicosidodecahedron
Type	Uniform polyhedron
Elements	F=112, E=180, V=60 (χ=-8)
Faces by sides	(40+60){3}+12{5/2}
Wythoff symbol	|3/2 3/2 5/2
Symmetry group	Ih
Index references	U72, C91, W118
(35.5/3)/2 (Vertex figure)	Small hexagrammic hexecontahedron (dual polyhedron)

In geometry, the small retrosnub icosicosidodecahedron is a nonconvex uniform polyhedron, indexed as U₇₂.

[edit] Cartesian coordinates

Cartesian coordinates for the vertices of a small retrosnub icosicosidodecahedron are all the even permutations of

(±½(−1/τ−√(3τ−2)), 0, ±½(3−τ√(3τ−2)))

(±½(1/τ−√(3τ−2)), ±1, ±½(1+2/τ−τ√(3τ−2)))

(±½(τ²−√(3τ−2)), ±1/τ, ±½(1−τ√(3τ−2)))

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

[edit] See also

• List of uniform polyhedra

[edit] External links

• Eric W. Weisstein, Small retrosnub icosicosidodecahedron at MathWorld.