Icosidodecadodecahedron
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| Icosidodecadodecahedron | |
|---|---|
 |
|
| Type | Uniform polyhedron |
| Elements | F = 44, E = 120 V = 60 (χ = -16) |
| Faces by sides | 12{5}+12{5/2}+20{6} |
| Wythoff symbol | 5/35 | 3 |
| Symmetry group | Ih |
| Index references | U44, C56, W83 |
 5.6.5/3.6 (Vertex figure) |
 Medial icosacronic hexecontahedron (dual polyhedron) |
In geometry, the icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U44.
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, its Wythoff symbol is 5/35 | 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 the vertex and edge arrangement, as well as its pentagonal and pentagrammic faces, with the rhombidodecadodecahedron.
