# Great ditrigonal icosidodecahedron

Great ditrigonal icosidodecahedron 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 ((3.5)3)/2
Bowers acronym Gidtid

In geometry, the great ditrigonal icosidodecahedron (or great ditrigonary icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U47. It has 4 Schwarz triangle equivalent constructions, for example Wythoff symbol 3 | 3 5/4 gives Coxeter diagram    =     . It has extended Schläfli symbol a{5/2,3} or c{3,5/2}, as an altered great stellated dodecahedron or converted great icosahedron.

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

## Related polyhedra

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.

a{5,3} a{5/2,3} b{5,5/2}    =         =           Small ditrigonal icosidodecahedron Great ditrigonal icosidodecahedron   