Icosidodecadodecahedron

In geometry, the icosidodecadodecahedron (or icosified dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U44. It has 44 faces (12 pentagons, 12 pentagrams and 20 hexagons), 120 edges and 60 vertices.[1] Its vertex figure is a crossed quadrilateral.

Icosidodecadodecahedron
TypeUniform star polyhedron
ElementsF = 44, E = 120
V = 60 (χ = 16)
Faces by sides12{5}+12{5/2}+20{6}
Coxeter diagram
Wythoff symbol5/3 5 | 3
5/2 5/4 | 3
Symmetry groupIh, [5,3], *532
Index referencesU44, C56, W83
Dual polyhedronMedial icosacronic hexecontahedron
Vertex figure
5.6.5/3.6
Bowers acronymIded
3D model of an icosidodecadodecahedron

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


See also

References

  1. Maeder, Roman. "44: icosidodecadodecahedron". MathConsult.


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