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The Kepler-Poinsot solids are the four regular concave polyhedra with intersecting facial planes. They are composed of regular convex or nonconvex polygons and were unknown to the ancients. Of the four only two can be built with Geomag parts augmented with 3/4 inch balls, the great stellated dodecahedron and small stellated dodecahedron.

The small stellated dodecahedron appeared ca. 1430 as a mosaic by Paolo Uccello on the floor of San Marco cathedral, Venice (Muraro 1955). The great stellated dodecahedron was published by Wenzel Jamnitzer in 1568. Kepler rediscovered these two (Kepler used the term "urchin" for the small stellated dodecahedron) and described them in his work Harmonice Mundi in 1619. The two known solids, great dodecahedron, and great icosahedron were subsequently (re)discovered by Poinsot in 1809. As shown by Cauchy, they are stellated forms of the dodecahedron and icosahedron.

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