Icosidodecadodecahedron

Icosidodecadodecahedron
File:Icosidodecadodecahedron.png
Type	Uniform star polyhedron
Elements	F = 44, E = 120 V = 60 (χ = −16)
Faces by sides	12{5}+12{5/2}+20{6}
Coxeter diagram	Template:CDD
Wythoff symbol	3 5/2 5/4 \| 3
Symmetry group	I_h, [5,3], *532
Index references	U₄₄, C₅₆, W₈₃
Dual polyhedron	Medial icosacronic hexecontahedron
Vertex figure	File:Icosidodecadodecahedron vertfig.png 5.6.5/3.6
Bowers acronym	Ided

3D model of an 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.

Related 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).

File:Rhombidodecadodecahedron convex hull.png Convex hull	File:Rhombidodecadodecahedron.png Rhombidodecadodecahedron	File:Icosidodecadodecahedron.png Icosidodecadodecahedron
File:Rhombicosahedron.png Rhombicosahedron	File:UC32-10 triangular prisms.png Compound of ten triangular prisms	File:UC33-20 triangular prisms.png Compound of twenty triangular prisms