Editing Dice (section)

====Common variations====
{{Further information|Isohedral figure{{!}}Isohedron}}
Dice are often sold in sets, matching in color, of six different shapes. Five of the dice are shaped like the [[Platonic solid]]s, whose faces are [[regular polygon]]s. Aside from the cube, the other four Platonic solids have 4, 8, 12, and 20 faces, allowing for those number ranges to be generated. The only other common non-cubical die is the 10-sided die, a [[pentagonal trapezohedron]] die, whose faces are ten [[kite (geometry)|kites]], each with two different edge lengths, three different angles, and two different kinds of vertices. 

Unlike other common dice, a [[four-sided die|four-sided (tetrahedral) die]] does not have a side that faces upward when it is at rest on a surface, so it must be read in a different way. On some four-sided dice, each face features multiple numbers, with the same number printed near each vertex on all sides. In this case, the number around the vertex pointing up is used. Alternatively, the numbers on a tetrahedral die can be placed at the middle of the edges, in which case the numbers around the base are used.

Normally, the faces on a die will be placed so opposite faces will add up to one more than the number of faces. (This is not possible with 4-sided dice and dice with an odd number of faces.) Some dice, such as those with 10 sides, are usually numbered sequentially beginning with 0, in which case the opposite faces will add to one less than the number of faces.

Using these dice in various ways, games can closely approximate a variety of [[probability distribution]]s. The percentile dice system is used to produce a [[Discrete uniform distribution|uniform distribution]] of random percentages, and summing the values of multiple dice will produce approximations to [[normal distribution]]s.<ref>{{Cite web |last1=Paret |first1=Michelle |last2=Martz |first2=Eston |year=2009 |title=Tumbling Dice & Birthdays: Understanding the Central Limit Theorem |url=http://www.minitab.com/uploadedFiles/Shared_Resources/Documents/Articles/CentralLimitTheorem.pdf |url-status=dead |archive-url=https://web.archive.org/web/20131101141751/http://www.minitab.com/uploadedFiles/Shared_Resources/Documents/Articles/CentralLimitTheorem.pdf |archive-date=1 November 2013 |access-date=29 September 2013 |publisher=Minitab}}</ref> 

{| class="wikitable"
|-
! Faces/sides
! colspan="2" | Shape
! Notes
|-
| [[Four-sided dice|4]] || [[Tetrahedron]] || [[File:Tetrahedron.png|48px|Tetrahedron]]
| 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 is usually thrown into the air instead {{Citation needed|date=April 2025}}.
|-
| 6 || [[Cube]] || [[File:Hexahedron.png|48px|Cube]]
| The most common variation of die. The sum of the numbers on opposite faces is 7.
|-
| 8 || [[Octahedron]] || [[File:Octahedron.png|48px|Octahedron]]
| Each face is triangular and the die resembles two [[square pyramid]]s attached base-to-base. Usually, the sum of the opposite faces is 9.
|-
| [[Ten-sided die|10]] || [[Pentagonal trapezohedron]] || [[File:Trapezohedron5.jpg|40px|Pentagonal trapezohedron]]
| Each face is a [[Kite (geometry)|kite]]. The die has two sharp corners, where five kites meet, and ten blunter corners, where three kites meet. Often, all [[Parity (mathematics)|odd numbered]] faces converge at one sharp corner, and the [[Parity (mathematics)|even]] ones at the other. The 10-sided die is usually numbered 0–9, though the 0 can also be read as a 10.
|-
| 12 || [[regular dodecahedron|Dodecahedron]] || [[File:Dodecahedron.png|48px|Dodecahedron]]
| Each face is a regular pentagon. The sum of the numbers on opposite faces is usually 13.
|-
| 20 || [[regular icosahedron|Icosahedron]] || [[File:Icosahedron.png|48px|Icosahedron]]
| Faces are [[equilateral triangle]]s. 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 0–9 twice as an alternative to 10-sided dice. The sum of the numbers on opposite faces is 21 if numbered 1–20.
|}