Great icosicosidodecahedron

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Great icosicosidodecahedron
Great icosicosidodecahedron.png
Type Uniform star polyhedron
Elements F = 52, E = 120
V = 60 (χ = 8)
Faces by sides20{3}+12{5}+20{6}
Coxeter diagram CDel label5.pngCDel branch 01rd.pngCDel split2-t3.pngCDel node 1.png
Wythoff symbol 3/2 5 | 3
3 5/4 | 3
Symmetry group Ih, [5,3], *532
Index references U 48, C 62, W 88
Dual polyhedron Great icosacronic hexecontahedron
Vertex figure Great icosicosidodecahedron vertfig.png
5.6.3/2.6
Bowers acronym Giid
3D model of a great icosicosidodecahedron Great icosicosidodecahedron.stl
3D model of a 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 pentagons, and 20 hexagons), 120 edges, and 60 vertices. [1] Its vertex figure is a crossed quadrilateral.

Contents

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.png
Truncated dodecahedron
Great icosicosidodecahedron.png
Great icosicosidodecahedron
Great ditrigonal dodecicosidodecahedron.png
Great ditrigonal dodecicosidodecahedron
Great dodecicosahedron.png
Great dodecicosahedron

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References

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