Icositruncated dodecadodecahedron

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Icositruncated dodecadodecahedron
Icositruncated dodecadodecahedron.png
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 Icositruncated dodecadodecahedron vertfig.png
Bowers acronym Idtid

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

Convex hull[edit]

Its convex hull is a nonuniform truncated icosidodecahedron.

Great rhombicosidodecahedron.png
truncated icosidodecahedron
Icositruncated dodecadodecahedron convex hull.png
Convex hull
Icositruncated dodecadodecahedron.png
Icositruncated dodecadodecahedron

Cartesian coordinates[edit]

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[edit]

Tridyakis icosahedron[edit]

Tridyakis icosahedron
DU45 tridyakisicosahedron.png
Type Star polyhedron
Face DU45 facets.png
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.

See also[edit]


  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208 Photo on page 96, Dorman Luke construction and stellation pattern on page 97.

External links[edit]