Great ditrigonal icosidodecahedron

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Great ditrigonal icosidodecahedron
Great ditrigonal icosidodecahedron.png
Type Uniform star polyhedron
Elements F = 32, E = 60
V = 20 (χ = −8)
Faces by sides 20{3}+12{5}
Wythoff symbol 3/2 | 3 5
3 | 3/2 5
3 | 3 5/4
3/2 | 3/2 5/4
Symmetry group Ih, [5,3], *532
Index references U47, C61, W87
Dual polyhedron Great triambic icosahedron
Vertex figure Great ditrigonal icosidodecahedron vertfig.png
Bowers acronym Gidtid

In geometry, the great ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U47. It has extended Schläfli symbol a{5/2,3} or c{3,5/2}, as an altered great stellated dodecahedron or converted great icosahedron, and Coxeter diagram CDel node h3.pngCDel 5-2.pngCDel node.pngCDel 3.pngCDel node.png. It has 4 Schwarz triangle equivalent constructions, for example Wythoff symbol 3 | 3/2 5, and Coxeter diagram Great ditrigonal icosidodecahedron cd.png.

Its circumradius is \frac{\sqrt{3}}{2} times the length of its edge,[1] a value it shares with the cube.

Related polyhedra[edit]

Its convex hull is a regular dodecahedron. It additionally shares its edge arrangement with the small ditrigonal icosidodecahedron (having the triangular faces in common), the ditrigonal dodecadodecahedron (having the pentagonal faces in common), and the regular compound of five cubes.

Small ditrigonal icosidodecahedron.png
Small ditrigonal icosidodecahedron
Great ditrigonal icosidodecahedron.png
Great ditrigonal icosidodecahedron
Ditrigonal dodecadodecahedron.png
Ditrigonal dodecadodecahedron
Dodecahedron (convex hull)
Compound of five cubes.png
Compound of five cubes


  1. ^ Weisstein, Eric W (2003), CRC concise encyclopedia of mathematics, Boca Raton: Chapman & Hall/CRC, ISBN 1-58488-347-2 

External links[edit]