Small retrosnub icosicosidodecahedron


In geometry, the small retrosnub icosicosidodecahedron is a nonconvex uniform polyhedron, indexed as U72. It has 112 faces, 180 edges, and 60 vertices. It is given a Schläfli symbol ß.
The 40 non-snub triangular faces form 20 coplanar pairs, forming star hexagons that are not quite regular. 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

for the vertices of a small retrosnub icosicosidodecahedron are all the even permutations of
where ϕ = /2 is the golden ratio and α =.