Small Rhombicosidodecahedron

An Archimedean Solid whose Dual Polyhedron is the Deltoidal Hexecontahedron. It has Schläfli Symbol r $\left\{{3\atop 5}\right\}$. It is also Uniform Polyhedron $U_{27}$ with Wythoff Symbol $3\,5\,\vert\,2$. Its faces are $20\{3\}+30\{4\}+12\{5\}$. The Small Dodecicosidodecahedron and Small Rhombidodecahedron are Faceted versions. The Inradius, Midradius, and Circumradius for $a=1$ are

$$r = {\textstyle{1\over 41}}(15+2\sqrt{5}\,)\sqrt{11+4\sqrt{5}} = 2.12099\ldots$$

$$\rho = {\textstyle{1\over 2}}\sqrt{10+4\sqrt{5}} = 2.17625\ldots$$

$$R = {\textstyle{1\over 2}}\sqrt{11+4\sqrt{5}} = 2.23295\ldots.$$

See also Great Rhombicosidodecahedron (Archimedean), Great Rhombicosidodecahedron (Uniform)