Polyhedron with 32 faces
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. It has 4 Schwarz triangle equivalent constructions, for example Wythoff symbol 3 | 3 ;templatestyles src="Fraction/styles.css" / ;5⁄4 gives Coxeter diagram = . It has extended Schläfli symbol a{ ;templatestyles src="Fraction/styles.css" / ;5⁄2,3} or c{3, ;templatestyles src="Fraction/styles.css" / ;5⁄2}, as an "altered great stellated dodecahedron" or "converted great icosahedron".
Its circumradius is formula_1 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.