Dice shapes

The most commonly used dice shapes are

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Tetrahedron: 4 faces

Each face has three numbers, arranged such that the upright number, placed either near the vertex or near the opposite edge, is the same on all three visible faces. The upright numbers represent the value of the roll. This die does not roll well and thus it is usually thrown into the air instead.

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Cube: 6 faces

A common die. The sum of the numbers on opposite faces is 7.

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Octahedron: 8 faces

Each face is triangular and the die resembles two square pyramids attached base-to-base. Usually, the sum of the opposite faces is 9.

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Pentagonal trapezohedron: 10 faces

Each face is a kite. The die has two sharp corners, where five kites meet, and ten blunter corners, where three kites meet.

The ten faces usually bear numbers from zero to nine, rather than one to ten (zero being read as "ten" in many applications).

Often all odd numbered faces converge at one sharp corner, and the even ones at the other.

The sum of the numbers on opposite faces is usually 9 (if numbered 0 to 9) or 11 (if numbered 1 to 10).

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Dodecahedron: 12 faces

Each face is a regular pentagon. The sum of the numbers on opposite faces is usually 13.

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Icosahedron: 20 faces

Faces are equilateral triangles. Icosahedra have been found dating to Roman/Ptolemaic times, but it is not known if they were used as gaming dice.

Modern dice with 20 sides are sometimes numbered 0 to 9 twice as an alternative to 10-sided dice.

The sum of the numbers on opposite faces is 21 if numbered 1 to 20.

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How random is a dice

Based on probability, a die should have an equal probability of landing on each of its faces.

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