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}
Coxeter diagram
Wythoff symbol	| 3/2 3/2 5/2
Symmetry group	Ih, [5,3], *532
Index references	U72, C91, W118
Dual polyhedron	Small hexagrammic hexecontahedron
Vertex figure	(35.5/3)/2
Bowers acronym	Sirsid

In geometry, the small retrosnub icosicosidodecahedron or small inverted retrosnub icosicosidodecahedron is a nonconvex uniform polyhedron, indexed as U₇₂. It is also called a retroholosnub icosahedron, ß{3/2,5}. Unlike most snub polyhedra, it has reflection symmetries.

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

(±(1-ϕ−α), 0, ±(3−ϕα))

(±(ϕ-1−α), ±2, ±(2ϕ-1−ϕα))

(±(ϕ+1−α), ±2(ϕ-1), ±(1−ϕα))

where ϕ = (1+√5)/2 is the golden ratio and α = √(3ϕ−2).

See also

• List of uniform polyhedra
• Small snub icosicosidodecahedron

External links

• Weisstein, Eric W. "Small retrosnub icosicosidodecahedron". MathWorld.
• Klitzing, Richard. "3D star small retrosnub icosicosidodecahedron".