Great Dirhombicosidodecahedron

The Uniform Polyhedron $U_{75}$ whose Dual is the Great Dirhombicosidodecacron. This Polyhedron is exceptional because it cannot be derived from Schwarz Triangles and because it is the only Uniform Polyhedron with more than six Polygons surrounding each Vertex (four Squares alternating with two Triangles and two Pentagrams). It has Wythoff Symbol $\vert\,{\textstyle{3\over 2}}\,{\textstyle{5\over 3}}\,3\,{\textstyle{5\over 2}}$. Its faces are $40\{3\}+60\{4\}+24\{{\textstyle{5\over 2}}\}$, and its Circumradius for unit edge length is

$$R={\textstyle{1\over 2}}\sqrt{2}\,.$$

References

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 200-203, 1989.