Type Uniform star polyhedron
Elements F = 44, E = 180
V = 120 (χ = −16)
Faces by sides 20{6}+12{10}+12{10/3}
Wythoff symbol 3 5 5/3 |
Symmetry group Ih, [5,3], *532
Index references U45, C57, W84
Dual polyhedron Tridyakis icosahedron
Vertex figure
6.10.10/3
Bowers acronym Idtid

In geometry, the icositruncated dodecadodecahedron or icosidodecatruncated icosidodecahedron is a nonconvex uniform polyhedron, indexed as U45.

## Convex hull

Its convex hull is a nonuniform truncated icosidodecahedron.

 truncated icosidodecahedron Convex hull Icositruncated dodecadodecahedron

## Cartesian coordinates

Cartesian coordinates for the vertices of an icositruncated dodecadodecahedron are all the even permutations of

(±(2−1/τ), ±1, ±(2+τ))
(±1, ±1/τ2, ±(3τ−1))
(±2, ±2/τ, ±2τ)
(±3, ±1/τ2, ±τ2)
(±τ2, ±1, ±(3τ−2))

where τ = (1+5)/2 is the golden ratio (sometimes written φ).

## Related polyhedra

### Tridyakis icosahedron

Tridyakis icosahedron
Type Star polyhedron
Face
Elements F = 120, E = 180
V = 44 (χ = −16)
Symmetry group Ih, [5,3], *532
Index references DU45