| Icosidodecadodecahedron | |
|---|---|
| Type | Uniform star polyhedron |
| Elements | F = 44, E = 120 V = 60 (χ = −16) |
| Faces by sides | 12{5}+12{5/2}+20{6} |
| Wythoff symbol | 5/3 5 | 3 |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U44, C56, W83 |
| Bowers acronym | Ided |
5.6.5/3.6 (Vertex figure) |
Medial icosacronic hexecontahedron (dual polyhedron) |
In geometry, the icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U44. Its vertex figure is a crossed quadrilateral.
The Icosidodecadodecahedron has 60 vertices, 120 edges, and 44 faces (12{5}+12{5/2}+20{6}). The vertex configuration is 5.6.5/3.6. Its symmetry group is Ih, [5,3], *532, its Wythoff symbol is 5/3 5 | 3, and its Euler characteristic is χ=−16.
Its uniform index number is U44, its Kaleido index is K49, its number in Wenninger's Polyhedron Models is 83, and it was given the number 56 in Coxeter's 1954 paper, which first gave the complete list of the uniform polyhedra.
It shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms. It additionally shares its edges with the rhombidodecadodecahedron (having the pentagonal and pentagrammic faces in common) and the rhombicosahedron (having the hexagonal faces in common).
convex hull |
Rhombidodecadodecahedron |
Icosidodecadodecahedron |
Rhombicosahedron |
Compound of ten triangular prisms |
Compound of twenty triangular prisms |