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
Symmetry group	Ih, [5,3], *532
Index references	U47, C61, W87
Bowers acronym	Gidtid
((3.5)3)/2 (Vertex figure)	Great triambic icosahedron (dual polyhedron)

In geometry, the great ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U₄₇.

The Great ditrigonal icosidodecahedron has 20 vertices, 60 edges, and 32 faces (20{3}+12{5}). The vertex configuration is ((3.5)³)/2. Its symmetry group is I_h, [5,3], *532, its Wythoff symbol is ³/₂ | 3 5, and its Euler characteristic is χ=−8.

Its uniform index number is U47, its Kaleido index is K52, its number in Wenninger's Polyhedron Models is 87, and it was given the number 61 in Coxeter's 1954 paper, which first gave the complete list of the uniform polyhedra.

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.

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

External links

• VRML model: [1]
• MathWorld