Three of these figures meet at each edge of the 120-cell, which consists of a total of 120 of these figures.
Three of these figures meet at each edge of the 120-cell, which consists of a total of 120 of these figures. The PoincarÃ© homology sphere and the Weber-Seifert space are constructed by applying two different amounts of twisting, and then gluing opposite portions of this figure. The SchlÃ¤fli symbol {5,3} corresponds to this figure. Three of the four objects named for Kepler and Poinsot are named for and derived from this figure, including the small and great stellated variants of it. It is possible to find a path that visits each of this figure's vertices precisely once and then ends back at the starting point, (*) a task that is the goal set by William Hamilton in the icosian game. For a prescribed volume, this figure has the smallest edge length of any regular, convex polyhedron. For 10 points, name this Platonic solid with 30 edges, which is the dual of the icosahedron, has faces that are regular pentagons, and has 12 faces.
Three of these figures meet at each edge of the 120-cell, which consists of a total of 120 of these figures.
(regular) dodecahedron 