The d120 is the ultimate fair die allowed by mathematics and this is the world's first injection-molded d120. It is based on a polyhedron known as the disdyakis triacontahedron. Each face is an elongated triangle. These dice are perfectly numerically balanced, with the same sums for numbers around vertices of the same type.
It can also be used as a dn, where n is any proper factor of 120, including all of the dice in a standard seven-dice polyset. This could be the only die you'll ever need.
120 is the maximum number of faces possible in an isohedron, excepting dipyramids and trapezohedra, which aren't workable solutions for physical dice with more than about 50 faces. Even requiring the pairing of opposing faces in conventional fashion, with 1 opposite 120, 2 opposite 119, etc, the number of possible numberings is astronomical. After weeks of searching with sophisticated techniques, Bob Bosch, a mathematician at Oberlin College, found a solution that perfectly balances the sums for all of the vertices. Twelve vertices have ten faces meeting at them, twenty have six faces, and thirty have four faces. In order to allow adequate space for numbers and firm settling on a face, the d120 is unusually large for a die.
Diameter = 2" (50 mm)
Weight = 0.2 lb. (95 gm.)
Colors = white, black, red, blue, green, purple, clear, & translucent amber
In geometry , a disdyakis triacontahedron, hexakis icosahedron, decakis dodecahedron or kisrhombic triacontahedron is a Catalan solid with 120 faces and the dual to the Archimedean truncated icosidodecahedron. As such it is face uniform but with irregular face polygons. It slightly resembles an inflated rhombic triacontahedron —if one replaces each face of the rhombic triacontahedron with a single vertex and four triangles in a regular fashion one ends up with a disdyakis triacontahedron. That is, the disdyakis triacontahedron is the Kleetope of the rhombic triacontahedron. It also has the most faces among the Archimedean and Catalan solids, with the snub dodecahedron, with 92 faces, in second place.
If the bipyramids and the trapezohedra are excluded, the disdyakis triacontahedron has the most faces of any other strictly convex polyhedron where every face of the polyhedron has the same shape. Projected into a sphere, the edges of a disdyakis triacontahedron define 15 great circles. Buckminster Fuller used these 15 great circles, along with 10 and 6 others in two other polyhedra to define his 31 great circles of the spherical icosahedron.