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.
Common dice
| 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 trapezohedron  | No | 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. 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 | dodecahedron  | Yes | Each face is a regular pentagon. |
| d20 | icosahedron  | Yes | Faces are equilateral triangles. Typically, opposite faces add to twenty-one. |
Uncommon dice
| Type | Shape | Notes |
|---|---|---|
| d7 | pentagonal 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 | 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.
Polyhedral dice in role-playing games
Dungeons & Dragons is noted for introducing the use of polyhedral dice during modern times. While the game uses traditional six-sided dice from time to time, other types of dice are used more frequently. The Third Edition of Dungeons & Dragons and the offshoot d20 System uses the d20 as a basic mechanic. Most types of dice are used for many different purposes (such as weapon damage, spell damage, saving throws, character generation, etc.).
Players use polyhedral dice together in a number of ways. For example, often a d10 is used in conjunction with a d6 instead of using a d20. If the d6 displays a 1-3, the number on the d10 is resolved as 1-10. If the d6 displays a 4-6, the number shown on the d10 is resolved to 11-20 ("1" is 11, "2" is 12, etc.). In cases like this, almost any sided die can be used as a "resolver." However, d6 are preferred as many players think they have the best "rolling" action (they don't roll too much, such as d20, d12, d10 or d8's may) and they actually roll, whereas d4's usually just sit where they are dropped. Hence a d8 is sometimes used in place of a d4 (1-2 on the d8 gives "1", 3-4 gives "2" etc.)
Almost any die can be used for a throw where a binary result (true or false) is needed. In these cases, the player calls the meaning of the result as the die is thrown, "One to three is true, four to six is false", or simply flips a coin. Some companies produce "binary dice" for just this niche — typically a d6 printed with plus and minus signs, or the words "even" and "odd."
Two d10 (or two d20) are used for probability throws where a 1-100 result is needed. When tossing these dice, the player indicates which dice is "high" (representing the tens position). For example, "red is high."
The Earthdawn game system pioneered "step die mechanics" through the use of its action step table. Generally speaking, a low skill is represented by a low die size, and a high skill is represented by a high die size. The Earthdawn table lists combinations of dice that are expected to produce average rolls from 1 to 40, and is used for almost all die-rolling in the game. Deadlands and The Window also make use of similar step die mechanics, though low abilities in The Window are represented by higher die types.
Both Vampire and Shadowrun use a "success test" mechanic, whereby the player rolls a certain number of the same kind of die (d6s in Shadowrun, d10s in Vampire), and only the dice that roll higher than a certain number are counted towards a successful test.
Several game systems allow dice to "open-end," whereby if a die shows the highest value, the player may roll the die again and add- sometimes without limit. Usually, the game system uses colorful lingo to describe this mechanic: In the swashbuckling RPG 7th Sea, dice explode; in the western-horror RPG Deadlands, such a die is said to be an ace.
Materials
It is unknown of what material the earliest polyhedral dice were made. A pair of icosahedral (20-sided) dice dating from Roman times are on display at the British Museum. It is possible that polyhedral dice were used by even earlier cultures.
Polyhedral dice are usually made of plastic, though infrequently metal, wooden, and semi-precious stone dice can be found. Early polyhedral dice were made of a soft plastic that would easily wear as the die was used. Typical wear and tear would gradually round the corners and edges of the die until it was unusable. Modern polyhedral dice are typically made of high impact plastic and can withstand years of use without visible wear. Lou Zocchi and his company Gamescience not only always guaranteed their high impact plastic dice to not wear down like other companies' dice did, but for years criticized major dice manufacturers of crafting unfair, loaded dice through sloppy polishing techniques and substandard materials.
Polyhedral dice can be purchased at most hobby stores in numerous combinations. In the early days of role-playing games, most dice came with the numbers unpainted and players took great care in painting their sets of dice. Many early d20's came with two sides with the numbers zero through nine on them; one side had to be painted a contrasting color to signify the "high" side.