Great ditrigonal icosidodecahedron

In geometry, the great ditrigonal 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 ${\displaystyle {\frac {\sqrt {3}}{2}}}$ times the length of its edge, a value it shares with the cube.

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