Home > Polyhedral dice
Polyhedral dice are dice with more or fewer than six sides, often used in games enjoyed by game enthusiasts, such as trading card games, German-style board games, and role-playing games. Although polyhedral dice are a relative novelty during modern times, some ancient cultures appear to have used them in games (as evidenced by the presence of two icosahedral dice dating from the days of ancient Rome on display in the British Museum).Polyhedral dice typically differ from standard six-sided dice in their markings: instead of the pips (dots) used to denote the value of each face, polyhedral dice are marked with a cardinal number on each side.
Such dice are referred to by the number of faces they have: a 'd6' (pronounced "dee-six") is a regular cubic die.
1 Common dice
Dice sold in sets are often identically colored, with matching die and marking colors. From left to right, the Platonic solids are the tetrahedron (d4), cube (d6), octahedron (d8), dodecahedron (d12) and icosahedron (d20). This set is missing a pentagonal trapezohedron (d10).
| Type | Shape | Platonic | Notes |
| d4 | tetrahedron | Yes | Each face has three numbers: they are arranged such that the upright number (which counts) is the same on all three visible faces. This die does not roll well and thus it is usually thrown into the air instead. |
| d6 | cube | Yes | A common die. The sum of the numbers on opposite faces is seven. |
| d8 | octahedron | Yes | Each face is triangular; looks something like two Egyptian pyramids attached at the base. |
| d10 | pentagonal trapezohedronpolyhedra The trapezohedra are the Dual polyhedrons of the antiprisms. None of the faces are trapezoids, so the name is misleading. A trapezohedron is also known as a deltohedron . A deltohedron should not be confused with a deltahedron (spelled with an " | No | Each face is kite-shapedA separate article is about kite flying. In geometry, a kite is a type of quadrilateral, a four-sided polygon. It has two pairs of equal sides, and the two sides in each pair are adjacent. contrast with the parallelogram, where the sides of each pair are; the smallest angle of five faces point to one edge, the smallest angle of the other points to the opposite. Often, all odd numbers are on one half of the die and all even numbers are on the other half. Additionally, on most currently-manufactured dice, faces on opposite halves of the die meet at a right angle. There is usually a face marked "0" but no face marked "10". |
| d12 | dodecahedronA dodecahedron is a Platonic solid composed of twelve pentagonal faces, with three meeting at each vertex. It has twenty vertices and thirty edges. Its dual polyhedron is the icosahedron. Canonical coordinates for the vertices of a dodecahedron centered a | Yes | Each face is a regular pentagon. |
| d20 | icosahedronAn icosahedron [aiks'hidrn] noun (plural: -drons, -dra [-dr]) is a polyhedron having 20 faces. The faces of a regular icosahedron are equilateral triangles. Etymology 16th Century: from Greek eikosaedron, from eikosi twenty + -edron -hedron], "icosa'hedra | Yes | Faces are equilateral triangles. Typically, opposite faces add to twenty-one. |
2 Uncommon dice
| Type | Shape | Notes |
| d7 | pentagonThis is an article about the geometrical shape. See The Pentagon for an article about the building near Washington, DC. See also: Pentagon (disambiguation). In geometry, a pentagon is any five-sided polygon. However, the term is commonly used to mean a real prism | A rare die type, thick enough to land either on its "edge" or "face". When landing on an edge, the topmost edge has pips for 1 through 5. The pentagonal faces are labeled with the digits 6 and 7. Such dice are used in a seven-player variant of backgammon. |
| d24 | tetrakis hexahedron | Each face is in the shape of an isosceles triangle. |
| d30 | rhombic triacontahedron | Each face is in the shape of a rhombus (diamond-shaped). |
d100
d% | Zocchihedron™ | True d100s are rare; they are nicknamed death stars due to a passing resemblance to the Star Wars ship. Two d10s can substitute for a d100, one of which may have sides labeled 00, 10, 20, ... 90. Use of this die, (or a replacement such as two different-colored d10s with there being a convention among players as to which of them will count as "tens" and which as "ones") is referred to as a percentile roll. |
Often the names of the dice appear in formulas for calculating game parameters: e.g., hit points. '6d8+10', for example, will yield a number between 16 (6×1+10) and 58 (6×8+10) with a binomial distribution, as it means 'Roll an eight-sided die six times and add ten to the total of all the rolls'. Occasionally they may be written '10×d6+20' or '1d6×10+20'; this means 'roll one six-sided die. Multiply it by ten and add twenty', and avoids boring repetitive dice-rolling at the expense of generating a binomial distribution.
