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 |
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.
Truncated icosidodecahedron |
Convex hull |
Icositruncated dodecadodecahedron |
Cartesian coordinates edit
Cartesian coordinates for the vertices of an icositruncated dodecadodecahedron are all the even permutations of
where is the golden ratio.
Related polyhedra edit
Tridyakis icosahedron edit
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 edit
- Catalan solid Duals to convex uniform polyhedra
- Uniform polyhedra
- List of uniform polyhedra
References 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