Inverted snub dodecadodecahedron


In geometry, the inverted snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U60. It is given a Schläfli symbol sr.

Cartesian coordinates

for the vertices of an inverted 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 negative real root of τα4−α3+2α2−α−1/τ, or approximately −0.3352090.
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 inverted pentagonal hexecontahedron

The medial inverted pentagonal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform inverted snub dodecadodecahedron. Its faces are irregular nonconvex pentagons, with one very acute angle.

Proportions

Denote the golden ratio by, and let be the largest real zero of the polynomial. Then each face has three equal angles of, one of and one of. Each face has one medium length edge, two short and two long ones. If the medium length is, then the short edges have length
and the long edges have length
The dihedral angle equals. The other real zero of the polynomial plays a similar role for the medial pentagonal hexecontahedron.