Dodecadodecahedron

The Uniform Polyhedron $U_{36}$ whose Dual Polyhedron is the Medial Rhombic Triacontahedron. The solid is also called the Great Dodecadodecahedron, and its Dual Polyhedron is also called the Small Stellated Triacontahedron. It can be obtained by Truncating a Great Dodecahedron or Faceting a Icosidodecahedron with Pentagons and covering remaining open spaces with Pentagrams (Holden 1991, p. 103). A Faceted version is the Great Dodecahemicosahedron. The dodecadodecahedron is an Archimedean Solid Stellation. The dodecadodecahedron has Schläfli Symbol $\{{\textstyle{5\over 2}}, 5\}$ and Wythoff Symbol $2\,\vert\,{\textstyle{5\over 2}}\,5$. Its faces are $12\{{\textstyle{5\over 2}}\}+12\{5\}$, and its Circumradius for unit edge length is

$$R=1.$$

References

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 123, 1989.

Holden, A. Shapes, Space, and Symmetry. New York: Dover, 1991.

Wenninger, M. J. Polyhedron Models. Cambridge, England: Cambridge University Press, p. 112, 1989.