Great Stellated Dodecahedron

One of the Kepler-Poinsot Solids whose Dual is the Great Icosahedron. Its Schläfli Symbol is $\{{\textstyle{5\over 2}}, 3\}$. It is also Uniform Polyhedron $U_{52}$ and has Wythoff Symbol $3\,\vert\,2\,{\textstyle{5\over 2}}$. Its faces are $12\{{\textstyle{5\over 2}}\}$. Its Circumradius for unit edge length is

$$R={\textstyle{1\over 2}}\sqrt{3}\,\phi^{-1} ={\textstyle{1\over 4}}\sqrt{3}(\sqrt{5}-1).$$

The easiest way to construct it is to make 12 Triangular Pyramids

with side length $\phi=(1+\sqrt{5}\,)/2$ (the Golden Ratio) times the base and attach them to the sides of an Icosahedron.

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

References

Fischer, G. (Ed.). Plate 104 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, p. 103, 1986.