The great stellated dodecahedron was published by Wenzel Jamnitzer in 1568. It was rediscovered by Kepler (and published in his work Harmonice Mundi in 1619),
and again by Poinsot in 1809.

The great stellated dodecahedron can be constructed from a unit dodecahedron by selecting the 144 sets of five coplanar vertices, then discarding sets whose edges
correspond to the edges of the original dodecahedron. This gives 12 pentagrams of
edge length ,
where
is the golden ratio. Rescaling to give the pentagrams
unit edge lengths, the circumradius of the great
stellated dodecahedron is

The skeleton of the great stellated dodecahedron is isomorphic to the dodecahedral
graph.

Another way to construct a great stellated dodecahedron via augmentation is to make 20 triangular pyramids with side length
(the golden ratio) times the base, as illustrated
above, and attach them to the sides of an icosahedron.
The height of these pyramids is then .

Cumulating a unit dodecahedron to construct a great
stellated dodecahedron produces a solid with edge lengths

Cauchy, A. L. "Recherches sur les polyèdres." J. de l'École Polytechnique9, 68-86, 1813.Cundy,
H. and Rollett, A. "Great Stellated Dodecahedron. ." §3.6.3 in Mathematical
Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 94-95, 1989.Fischer,
G. (Ed.). Plate 104 in Mathematische
Modelle aus den Sammlungen von Universitäten und Museen, Bildband. Braunschweig,
Germany: Vieweg, p. 103, 1986.Jamnitzer, W. Perspectiva Corporum
Regularium. Nürnberg, Germany, 1568. Reprinted Frankfurt, 1972.Kasahara,
K. Origami
Omnibus: Paper-Folding for Everyone. Tokyo: Japan Publications, p. 239,
1988.Kepler, J. "Harmonice Mundi." In Opera
Omnia, Vol. 5. Frankfurt, 1864.Wenninger, M. J. Dual
Models. Cambridge, England: Cambridge University Press, pp. 39-40, 1983.Wenninger,
M. J. Polyhedron
Models. Cambridge, England: Cambridge University Press, pp. 35 and 40,
1989.