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Polyhedral dice

In a wide variety of role playing games, a number of polyhedral dice are used. The commonest are in the shapes of the five Platonic solids.

Typically, these dice are referred to by the number of faces they have: a 'd6' is a regular cubic die, pronounced 'dee-six'.

Common Dice:
d4tetrahedronEach face has three numbers: they are arranged such that the top number is the same on all three visible faces.Yes
d6cubeA common die. Opposite faces must add to seven.Yes
d8octahedronEach face is triangular; looks something like two Egyptian pyramids attached at the base.Yes
d10Irregular decahedron;
see Dice/10-sided dice
Each face is kite-shaped; the smallest angle of five faces point to one edge, the smallest angle of the other points to the opposite. Not a regular polyhedron. Often, all odd number are on one half of the die and all even faces are on the other half.No
d12dodecahedronEach face is a regular pentagon.Yes
d20icosahedronFaces are equilateral triangles. Typically, opposite faces add to twenty-one.Yes

Uncommon Dice:
d7A very uncommon die type, it's shaped as a pentagonal prism, 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.
d30Each face is in the shape of a rhombus (diamond-shaped).
Trade name: ZocchihedronUsually modelled by rolling two d10, one labelled 00,10,20..90, the other normal. Examples do exist of 'true' d100's, but these are rare, and given the nickname death stars due to a passing resemblance to the Star Wars ship. Other d100s may be in the shape of a golf ball.

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 bell curve 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 bell curve distribution.