Great Dodecahedron

$\begin{figure}\begin{center}\BoxedEPSF{great_dodecahedron_net.epsf scaled 700}\end{center}\end{figure}$

The Uniform Polyhedron $U_{35}$ which is the Dual of the Small Stellated Dodecahedron and one of the Kepler-Poinsot Solids. Its faces are $12\{5\}$ . Its Schläfli Symbol is $\{5, {\textstyle{5\over 2}}\}$ , and its Wythoff Symbol is ${\textstyle{5\over 2}}\,\vert\,2\,5$ . Its faces are $12\{5\}$ . Its Circumradius for unit edge length is

$\begin{displaymath} R={\textstyle{1\over 2}}5^{1/4} \phi^{1/2} a={\textstyle{1\over 4}}5^{1/4}\sqrt{2(1+\sqrt{5})}\,, \end{displaymath}$

where $\phi$ is the Golden Ratio.

References

Fischer, G. (Ed.). Plate 105 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, p. 104, 1986.