Great icosicosidodecahedron

In geometry, the great icosicosidodecahedron (or great icosified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U48. Its vertex figure is a crossed quadrilateral.

Great icosicosidodecahedron
TypeUniform star polyhedron
ElementsF = 52, E = 120
V = 60 (χ = 8)
Faces by sides20{3}+12{5}+20{6}
Wythoff symbol3/2 5 | 3
3 5/4 | 3
Symmetry groupIh, [5,3], *532
Index referencesU48, C62, W88
Dual polyhedronGreat icosacronic hexecontahedron
Vertex figure
Bowers acronymGiid

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

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