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Small Stellated Dodecahedron


One of the Kepler-Poinsot Solids whose Dual Polyhedron is the Great Dodecahedron. Its Schläfli Symbol is $\{{\textstyle{5\over 2}}, 5\}$. It is also Uniform Polyhedron $U_{34}$ and has Wythoff Symbol $5\,\vert\,2\,{\textstyle{5\over 2}}$. It was originally called the Urchin by Kepler. It is composed of 12 Pentagrammic faces. Its faces are $12\{{\textstyle{5\over 2}}\}$. The easiest way to construct it is to build twelve pentagonal Pyramids

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

and attach them to the faces of a Dodecahedron. The Circumradius of the small stellated dodecahedron with $a=1$ is

R={\textstyle{1\over 2}}5^{1/4}\phi^{-1/2} ={\textstyle{1\over 4}}5^{1/4}\sqrt{2(\sqrt{5}-1)}\,.

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


Fischer, G. (Ed.). Plate 103 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, p. 102, 1986.

Rawles, B. Sacred Geometry Design Sourcebook: Universal Dimensional Patterns. Nevada City, CA: Elysian Pub., p. 219, 1997.

© 1996-9 Eric W. Weisstein