Great icosicosidodecahedron

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.[1] 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
3 5/4 | 3
Symmetry groupIh, [5,3], *532
Index referencesU48, C62, W88
Dual polyhedronGreat icosacronic hexecontahedron
Vertex figure
5.6.3/2.6
Bowers acronymGiid
3D model of a great icosicosidodecahedron

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

References

  1. Maeder, Roman. "48: great icosicosidodecahedron". MathConsult.


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