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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.
Contents
Convex hull
Its convex hull is a nonuniform truncated dodecahedron.
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).
References
Small retrosnub icosicosidodecahedron Wikipedia(Text) CC BY-SA