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
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
Wythoff symbol	5/3 5 | 3 5/2 5/4 | 3
Symmetry group	Ih, [5,3], *532
Index references	U44, C56, W83
Dual polyhedron	Medial icosacronic hexecontahedron
Vertex figure	5.6.5/3.6
Bowers acronym	Ided

3D model of an icosidodecadodecahedron

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).

Convex hull	Rhombidodecadodecahedron	Icosidodecadodecahedron
Rhombicosahedron	Compound of ten triangular prisms	Compound of twenty triangular prisms

See also

• List of uniform polyhedra
• Snub icosidodecadodecahedron