Small retrosnub icosicosidodecahedron

Small retrosnub icosicosidodecahedron
Type	Uniform star 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, [5,3], *532
Index references	U72, C91, W118
Bowers acronym	Sirsid
(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.

Convex hull

Its convex hull is a nonuniform truncated dodecahedron.

truncated dodecahedron

Convex hull

Small retrosnub icosicosidodecahedron

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).

See also

• List of uniform polyhedra
• Small snub icosicosidodecahedron

External links

• Weisstein, Eric W., "Small retrosnub icosicosidodecahedron" from MathWorld.