 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.

## 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
dual polyhedron Icositruncated dodecadodecahedron

The tridyakis icosahedron is the dual polyhedron of the nonconvex uniform polyhedron, icositruncated dodecadodecahedron. It has 44 vertices, 180 edges, and 120 scalene triangular faces.