Snub icosidodecadodecahedron


In geometry, the snub icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U46. It has 104 faces, 180 edges, and 60 vertices.
As the name indicates, it belongs to the family of snub polyhedra.

Cartesian coordinates

for the vertices of a snub icosidodecadodecahedron are all the even permutations of
with an even number of plus signs, where
and where τ = /2 is the golden mean and
ρ is the real solution to ρ3=ρ+1, or approximately 1.3247180.
ρ is called the plastic constant.
Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one.

Related polyhedra

Medial hexagonal hexecontahedron

The medial hexagonal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform snub icosidodecadodecahedron.