Snub Dodecadodecahedron

The Uniform Polyhedron $U_{40}$ whose Dual Polyhedron is the Medial Pentagonal Hexecontahedron. It has Wythoff Symbol $\vert\,2\,{\textstyle{5\over 2}}\,5$. Its faces are $12\{{\textstyle{5\over 2}}\}+60\{3\}+12\{5\}$. It has Circumradius for $a=1$ of

$$R=1.27443994.$$

See also Snub Cube

References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 139, 1987.

Coxeter, H. S. M.; Longuet-Higgins, M. S.; and Miller, J. C. P. ``Uniform Polyhedra.'' Phil. Trans. Roy. Soc. London Ser. A 246, 401-450, 1954.

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, pp. 174-176, 1971.