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
Dual polyhedron Medial pentagonal hexecontahedron
Vertex figure
3.3.5/2.3.5
Bowers acronym Siddid

In geometry, the snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U40. It is given a Schläfli symbol sr{5/2,5}, as a snub great dodecahedron.

## Cartesian coordinates

Cartesian coordinates for the vertices of a snub dodecadodecahedron are all the even permutations of

(±2α, ±2, ±2β),
(±(α+β/τ+τ), ±(-ατ+β+1/τ), ±(α/τ+βτ-1)),
(±(-α/τ+βτ+1), ±(-α+β/τ-τ), ±(ατ+β-1/τ)),
(±(-α/τ+βτ-1), ±(α-β/τ-τ), ±(ατ+β+1/τ)) and
(±(α+β/τ-τ), ±(ατ-β+1/τ), ±(α/τ+βτ+1)),

with an even number of plus signs, where

β = (α2/τ+τ)/(ατ−1/τ),

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.

## Related polyhedra

### Medial pentagonal hexecontahedron

Medial pentagonal hexecontahedron
Type Star polyhedron
Face
Elements F = 60, E = 150
V = 84 (χ = −6)
Symmetry group I, [5,3]+, 532
Index references DU40