Snub dodecadodecahedron


In geometry, the snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U40. It has 84 faces, 150 edges, and 60 vertices. It is given a Schläfli symbol sr{,5}, as a snub great dodecahedron.

Cartesian coordinates

for the vertices of a snub dodecadodecahedron are all the even permutations of
with an even number of plus signs, where
where τ = /2 is the golden mean and
α is the positive real root of τα4−α3+2α2−α−1/τ, or approximately 0.7964421.
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 pentagonal hexecontahedron

The medial pentagonal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the snub dodecadodecahedron. It has 60 intersecting irregular pentagonal faces.