| Snub dodecadodecahedron | |
|---|---|
| Type | Uniform star polyhedron |
| Elements | F = 84, E = 150 V = 60 (χ = −6) |
| Faces by sides | 60{3}+12{5}+12{5/2} |
| Wythoff symbol | |2 5/2 5 |
| Symmetry group | I, [5,3]+, 532 |
| Index references | U40, C49, W111 |
| Bowers acronym | Siddid |
3.3.5/2.3.5 (Vertex figure) |
Medial pentagonal hexecontahedron (dual polyhedron) |
In geometry, the snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U40. It is given a Schläfli symbol s{5/2,5}, 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 = (1+√5)/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.
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