# Great icosicosidodecahedron

Great icosicosidodecahedron Type Uniform star polyhedron
Elements F = 52, E = 120
V = 60 (χ = −8)
Faces by sides 20{3}+12{5}+20{6}
Wythoff symbol 3/2 5 | 3
3 5/4 | 3
Symmetry group Ih, [5,3], *532
Index references U48, C62, W88
Dual polyhedron Great icosacronic hexecontahedron
Vertex figure 5.6.3/2.6
Bowers acronym Giid

In geometry, the great icosicosidodecahedron (or great icosified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U48. It has 52 faces (20 triangles, 12 pentagrams, and 20 hexagons), 120 edges, and 60 vertices. Its vertex figure is a crossed quadrilateral.

## Related polyhedra

It shares its vertex arrangement with the truncated dodecahedron. It additionally shares its edge arrangement with the great ditrigonal dodecicosidodecahedron (having the triangular and pentagonal faces in common) and the great dodecicosahedron (having the hexagonal faces in common). Truncated dodecahedron Great icosicosidodecahedron Great ditrigonal dodecicosidodecahedron Great dodecicosahedron