# Dice Cup - Variants - Non-cubic - Rarer Variations

Rarer Variations

Sides Shape Notes
1 sphere Most commonly a joke die, this is just a sphere with a 1 marked on it. See also: non-cubical dice, Monostatic polytope, and Gömböc.
2 cylinder This is nothing more than a coin shape with 1 marked on one side and 2 on the other. While some tasks in roleplaying require flipping a coin, the game rules usually simply call for the use of a coin rather than requiring the use of a two-sided die. It is possible, however, to find dice of this sort for purchase, but they are rare, and can typically be found among other joke dice.
3 Rounded-off triangular prism This is a rounded-off triangular prism, intended to be rolled like a rolling-pin style die. The die is rounded-off at the edges to make it impossible for it to somehow land on the triangular sides, which makes it look a bit like a jewel. When the die is rolled, one edge (rather than a side) appears facing upwards. On either side of each edge the same number is printed (from 1 to 3). The numbers on either side of the up-facing edge are read as the result of the die roll. Another possible shape is the "American Football" or "Rugby ball" shape, where the ends are pointed (with rounded points) rather than just rounded. A third variety features faces that resemble warped squares.
5 Triangular prism This is a prism that is thin enough to land either on its "edge" or "face". When landing on an edge, the result is displayed by digits (2–4) close to the prism's top edge. The triangular faces are labeled with the digits 1 and 5.
7 Pentagonal prism Similar in constitution to the 5-sided die. When landing on an edge, the topmost edge has pips for 1–5. The pentagonal faces are labeled with the digits 6 and 7. This kind of die is particularly odd since it has pips for five of its results and digits for two of them. Seven-sided dice are used in a seven-player variant of backgammon. Some variants have heptagonal ends and rectangular faces.
12 rhombic dodecahedron Each face is a rhombus.
14 heptagonal trapezohedron Each face is a kite.
16 octagonal dipyramid Each face is an isosceles triangle.
24 tetrakis hexahedron Each face is an isosceles triangle.
24 deltoidal icositetrahedron Each face is a kite.
30 rhombic triacontahedron Each face is a rhombus. Although not included in most dice kits, it can be found in most hobby and game stores.
34 heptadecagonal trapezohedron Each face is a kite.
50 icosakaipentagonal trapezohedron The faces of the 50-sided die are kites, although very narrow.
60 pentakis dodecahedron
100 Zocchihedron 100-sided dice can be found in hobby and game stores. They are not, however, a true polyhedron. A 100-sided die is made by flattening 100 facets on a sphere.

The full geometric set of "uniform fair dice" (face-transitive) are:

• Platonic solids, the five regular polyhedra: 4, 6, 8, 12, 20 sides
• Catalan solids, the duals of the 13 Archimedean solids: 12, 24, 30, 48, 60, 120 sides
• Bipyramids, the duals of the infinite set of prisms, with triangle faces: any even number above 4
• Trapezohedrons, the duals of the infinite set of antiprisms, with kite faces: any even number above 4
• Disphenoids, an infinite set of tetrahedra made from congruent non-regular triangles: 4 sides
• "Rolling-pin style dice" are the only way to make dice with an odd number of flat faces. They are based on an infinite set of prisms. All the (rectangular) faces they may actually land on are congruent, so they are equally fair. (The other 2 sides of the prism are rounded or capped with a pyramid, designed so that the die never actually rests on those faces.)