Icositruncated dodecadodecahedron
Polyhedron with 44 faces
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
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
where is the golden ratio.
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 icositruncated dodecadodecahedron. It has 44 vertices, 180 edges, and 120 scalene triangular faces.
See also
- Catalan solid Duals to convex uniform polyhedra
- Uniform polyhedra
- List of uniform polyhedra
References
- 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
- Weisstein, Eric W. "Icositruncated dodecadodecahedron". MathWorld.
- v
- t
- e
polyhedra (nonconvex
regular polyhedra)
of Kepler-Poinsot
polyhedra
hemipolyhedra
uniform polyhedra
- medial rhombic triacontahedron
- small stellapentakis dodecahedron
- medial deltoidal hexecontahedron
- small rhombidodecacron
- medial pentagonal hexecontahedron
- medial disdyakis triacontahedron
- great rhombic triacontahedron
- great stellapentakis dodecahedron
- great deltoidal hexecontahedron
- great disdyakis triacontahedron
- great pentagonal hexecontahedron
uniform polyhedra with
infinite stellations
This polyhedron-related article is a stub. You can help Wikipedia by expanding it. |
- v
- t
- e