Editing Dice (section)

====Rarer variations====
[[Image:Dices collection.png|upright=1.9|thumb|Dice collection: D2–D22, D24, D26, D28, D30, D36, D48, D50, D60 and D100.]]

"Uniform fair dice" are dice where all faces have an equal probability of outcome due to the symmetry of the die as it is [[isohedral figure|face-transitive]]. In addition to the Platonic solids, these theoretically include:

* [[Catalan solid]]s, the [[dual polyhedron|duals]] of the 13 [[Archimedean solid]]s: 12, 24, 30, 48, 60, 120 sides
* [[Trapezohedron|Trapezohedra]], the duals of the infinite set of [[antiprism]]s, with kite faces: any even number not divisible by 4 (so that a face will face up), starting from 6
* [[Bipyramid]]s, the duals of the infinite set of [[Prism (geometry)|prisms]], with triangle faces: any multiple of 4 (so that a face will face up), starting from 8
* [[Disphenoid]]s, an infinite set of tetrahedra made from congruent non-regular triangles: 4 sides. This is a less symmetric tetrahedron than the Platonic tetrahedron but still sufficiently symmetrical to be face-transitive. Similarly, [[Pyritohedron|pyritohedra]] and [[tetartoid]]s are less symmetrical but still face-transitive dodecahedra: 12 sides.

Two other types of polyhedra are technically not face-transitive but are still fair dice due to symmetry:

* [[antiprism]]s: the basis of [[barrel dice]]
* [[prism (geometry)|prism]]s: the basis of long dice and teetotums

[[Long dice]] and [[teetotum]]s can, in principle, be made with any number of faces, including odd numbers.<ref>{{Cite web |last=Kybos |first=Alea |title=Properties of Dice |url=http://www.aleakybos.ch/Properties%20of%20Dice.pdf |url-status=dead |archive-url=https://web.archive.org/web/20120528013233/http://www.aleakybos.ch/Properties%20of%20Dice.pdf |archive-date=28 May 2012 |access-date=7 October 2012}}</ref> Long dice are based on the infinite set of [[prism (geometry)|prisms]]. All the rectangular faces are mutually face-transitive, so they are equally probable. The two ends of the prism may be rounded or capped with a pyramid, designed so that the die cannot rest on those faces. 4-sided long dice are easier to roll than tetrahedra and are used in the traditional board games [[dayakattai]] and [[daldøs]].

{| class="wikitable"
|-
! Faces/sides
! Shape
! Image
! Notes
|-
| 1
| [[Möbius strip]] or [[sphere]]
| [[File:D1 dice.JPG|48px]]
| Most commonly a [[practical joke|joke]] die, this is either a sphere with a 1 marked on it or shaped like a [[Möbius strip]]. It entirely defies the aforementioned use of a die.
|-
| 2
| Flat [[Cylinder (geometry)|Cylinder]] or Flat [[Prism_(geometry)|Prism]]
|[[File:D02.JPG|48x48px]]
| A [[coin flip]]. Some coins with 1 marked on one side and 2 on the other are available, but most simply use a common coin. (See also [[Binary lot]].)
|-
| 3
| Rounded-off [[triangular prism]]
| [[File:D03 wood.jpg|48px]]
| A long die intended to be rolled lengthwise. 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.
|-
| 4
| Capped 4-sided [[long die]]
| [[File:Daldøs die.jpg|48px]]
| A long die intended to be rolled lengthwise. It cannot stand on end as the ends are capped.
|-
| rowspan=3 | 5
|-
| [[Triangular prism]]
| [[File:D05.jpg|48px]]
| A prism 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 - similar to a 4-sided die. The triangular faces are labeled with the digits 1 and 5. 
|-
| Capped 5-sided [[long die]]
| [[File:Game of Dignitaries long die Culin 1898 fig 136.png|48px]]
| Five-faced long die for the Korean Game of Dignitaries; notches indicating values are cut into the edges, since in an odd-faced long die these land uppermost.
|-
| 6
| Capped 6-sided [[long die]]
| [[File:Owzthat Dice Game.jpg|48px]]
| Two six-faced long dice are used to simulate the activity of scoring runs and taking wickets in the game of [[cricket]]. Originally played with labeled six-sided pencils, and often referred to as [[pencil cricket]].
|-
| rowspan=2 | 7
| [[Pentagonal prism]]
| [[File:D07.jpg|48px]]
| Similar in constitution to the 5-sided die. Seven-sided dice are used in a [[Seven-sided backgammon|seven-player variant]] of [[backgammon]]. Seven-sided dice are described in the 13th century {{lang|es|[[Libro de los juegos]]}} as having been invented by [[Alfonso X of Castile|Alfonso X]] in order to speed up play in [[chess variants]].<ref>{{Cite web |title=games.rengeekcentral.com |url=http://games.rengeekcentral.com/tc4.html |access-date=18 June 2012 |publisher=games.rengeekcentral.com}}</ref><ref>{{Cite web |title=wwmat.mat.fc.ul.pt |url=http://wwmat.mat.fc.ul.pt/~jnsilva/HJT2k9/AlfonsoX.pdf |archive-url=https://web.archive.org/web/20110302034551/http://wwmat.mat.fc.ul.pt/~jnsilva/HJT2k9/AlfonsoX.pdf |archive-date=2011-03-02 |url-status=live |access-date=18 June 2012 }}</ref> 
|-
| [[Spherical_cap|Truncated sphere]]
| [[File:D7_dice.JPG|48px]]
| A truncated sphere with seven landing positions. 
|-
| 9
| Truncated sphere
| [[File:D9-dice-impact.png|48px]]
| A truncated sphere with nine landing positions. 
|-
| 10
| Decahedron
| [[File:D10_truncated.jpg|48px]]
| A ten-sided die made by truncating two opposite vertices of an octahedron. 
|-
| 11
| Truncated sphere
| [[File:D11_dice.JPG|48px]]
| A truncated sphere with eleven landing positions. 
|-
| 12
| [[Rhombic dodecahedron]]
| [[File:D12_rhombic_dodecahedron.JPG|48px]]
| Each face is a [[rhombus]].
|-
| 13
| Truncated sphere
| [[File:D13_dice.JPG|48px]]
| A truncated sphere with thirteen landing positions. 
|-
| rowspan=3 | 14
| [[Heptagonal trapezohedron]]
| [[File:14面体ダイス.jpg|48px]]
| Each face is a [[kite (geometry)|kite]].
|-
| [[Truncated octahedron]]
| [[File:Korean14dice2.JPG|48px]]
| A truncated octahedron. Each face is either a square or a hexagon. 
|-
| Truncated sphere
| [[File:D14_truncated_octahedron.jpg|48px]]
| A truncated sphere with fourteen landing positions. The design is based on the [[cuboctahedron]]. 
|-
| 15
| Truncated sphere
| [[File:D15_dice.JPG|48px]]
| A truncated sphere with fifteen landing positions. 
|-
| 16
| [[Octagonal bipyramid]]
| [[File:D16_dice.JPG|48px]]
| Each face is an isosceles triangle.
|-
| 17
| Truncated sphere
| [[File:D17_dice_2.JPG|48px]]
| A truncated sphere with seventeen landing positions. 
|-
| 18
| Rounded [[rhombicuboctahedron]]
| [[File:D18_rhombicuboctahedron.JPG|48px]]
| Eighteen faces are squares. The eight triangular faces are rounded and cannot be landed on. 
|-
| 19
| Truncated sphere
| [[File:D19_dice.JPG|48px]]
| A truncated sphere with nineteen landing positions. 
|-
| 21
| Truncated sphere
| [[File:D21_dice.webp|48px]]
| A truncated sphere with twenty-one landing positions. 
|-
| 22
| Truncated sphere
| [[File:D22_dice.JPG|48px]]
| A truncated sphere with twenty-two landing positions. 
|-
| rowspan=5 | 24
| [[Triakis octahedron]]
| [[File:D24_triakis_octahedron_dice.JPG|48px]]
| Each face is an isosceles triangle.
|-
| [[Tetrakis hexahedron]]
| [[File:D24_tetrakis_hexahedron.JPG|48px]]
| Each face is an isosceles triangle.
|-
| [[Deltoidal icositetrahedron]]
| [[File:D24_deltoidal_icositetrahedron.JPG|48px]]
| Each face is a kite.
|-
| Pseudo-deltoidal icositetrahedron
| [[File:D24 pseudo uniform polyhedrondice.jpg|48px]]
| Each face is a kite.
|-
| [[Pentagonal icositetrahedron]]
| [[File:D24_pentagonal_icositetrahedron_dice.JPG|48px]]
| Each face is an irregular pentagon.
|-
| 26
| Truncated sphere
| [[File:D26_dice.webp|48px]]
| A truncated sphere with twenty-six landing positions.  
|-
| 28
| Truncated sphere
| [[File:D28_dice.webp|48px]]
| A truncated sphere with twenty-eight landing positions. 
|-
| 30
| [[Rhombic triacontahedron]]
| [[File:D30.jpg|48px]]
| Each face is a rhombus.
|-
| 32
| Truncated sphere
| [[File:D32_dice.JPG|48px]]
| A truncated sphere with thirty-two landing positions. The design is similar to that of a [[truncated icosahedron]]. 
|-
| 34
| [[Heptadecagon]]al trapezohedron
| [[File:D34.jpg|48px]]
| Each face is a kite.
|-
| 36
| Truncated sphere
| [[File:D36_dice.webp|48px]]
| A truncated sphere with thirty-six landing positions. Rows of spots are present above and below each number 1 through 36 so that this die can be used to roll two six-sided dice simultaneously. 
|-
| 48
| [[Disdyakis dodecahedron]]
| [[File:D48_dice.JPG|48px]]
| Each face is a [[scalene triangle]].
|-
| 50
| Icosipentagonal trapezohedron
| [[File:D50 trapezohedron dice.JPG|48px]]
| Each face is a kite.
|-
| rowspan=4 | 60
| [[Deltoidal hexecontahedron]]
| [[File:D60_60men-saikoro.JPG|48px]]
| Each face is a kite.
|-
| [[Pentakis dodecahedron]]
| [[File:D60_pentakis_dodecahedron_dice.JPG|48px]]
| Each face is an isosceles triangle.
|-
| [[Pentagonal hexecontahedron]]
| [[File:D60_pentagonal_hexecontahedron_dice.JPG|48px]]
| Each face is an irregular pentagon.
|-
| [[Triakis icosahedron]]
| [[File:D60_triakis_icosahedron_dice.JPG|48px]]
| Each face is an isosceles triangle.
|-
| 100
| [[Zocchihedron]]
| [[File:Zocchihedron2.jpg|48px]]
| A sphere containing another sphere with 100 facets flattened into it. Note that this design is not isohedral; it does not function as a uniform fair die as some results are more likely than others.
|-
| 120
| [[Disdyakis triacontahedron]]
| [[File:D120.jpg|48px]]
| Each face is a scalene triangle.
|}