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Icositruncated dodecadodecahedron

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Icositruncated dodecadodecahedron
Type Uniform star polyhedron
Elements F = 44, E = 180
V = 120 (χ = −16)
Faces by sides 20{6}+12{10}+12{10/3}
Coxeter diagram
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
3D model of an icositruncated dodecadodecahedron

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

Convex hull

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Its convex hull is a nonuniform truncated icosidodecahedron.


Truncated icosidodecahedron

Convex hull

Icositruncated dodecadodecahedron

Cartesian coordinates

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

where is the golden ratio.

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Tridyakis icosahedron

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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 icositruncated dodecadodecahedron. It has 44 vertices, 180 edges, and 120 scalene triangular faces.

See also

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References

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  • 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.
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