Great ditrigonal icosidodecahedron

In geometry, the great ditrigonal icosidodecahedron (or great ditrigonary icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U₄₇. It has 32 faces (20 triangles and 12 pentagons), 60 edges, and 20 vertices.^[1] 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.

Great ditrigonal icosidodecahedron
Type	Uniform star polyhedron
Elements	F = 32, E = 60 V = 20 (χ = −8)
Faces by sides	20{3}+12{5}
Coxeter diagram
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

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