Great Icosahedron

One of the Kepler-Poinsot Solids whose Dual is the Great Stellated Dodecahedron. Its faces are $20\{3\}$. It is also Uniform Polyhedron $U_{53}$ and has Wythoff Symbol $3\,{\textstyle{5\over 2}}\,\vert\,{\textstyle{5\over 3}}$. Its faces are $20\{3\}+12\{{\textstyle{5\over 2}}\}+12\{{\textstyle{10\over 3}}\}$. Its Circumradius for unit edge length is

$$R={\textstyle{1\over 2}}\sqrt{11-4\sqrt{5}}\,.$$

See also Great Dodecahedron, Great Stellated Dodecahedron, Kepler-Poinsot Solid, Small Stellated Dodecahedron, Truncated Great Icosahedron

References

Fischer, G. (Ed.). Plate 106 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, p. 105, 1986.

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, p. 154, 1989.