Furthermore fair dice? In the field of board games, it is immediately apparent that fair die can be constructed for 2, 4, 6, 8, 10, 12 and 20 sides; represented by the coin, tetrahedron, cube, octahedron, decahedron, dodecahedron and icosahedron, respectively.
However, can a fair die be constructed for an arbitrary number of outcomes; say, for instance, a 7-sided die?
 A: According to Wikipedia every dice with a number sides of greater 4 and even is a fair dice. 2 and 4 (coin and tetrahedron) are of course fair too. Now we have two options to construct dice with uneven numbered sides:
1. We take an even sided dice with n sides and label number it from $1$ to $n/2$ twice, which, or 
2. We construct a regular k-sided prism and round the edges so we get k sides which all have equal probability for the die to land on.
A: There is a solution for a fair die for any number $n$ of faces. The obvious answer is a rolling prism with an $n$-sided polygon cross-section. However, if you want to disallow this because of the two extra faces on the top and bottom which actually have a nonzero chance of being selected, you can have an $(n-2)$-sided polygon cross-section.
Assuming a fixed cross-section, you can then adjust the length of the prism for the probabilities of all the faces to be equal: a very flat prism is essentially a coin and has near-$1$ probability of landing on one of the two $(n-2)$-sided faces, whereas a very long one has a near-$0$ chance of this happening. There must therefore be a length for which the probability of landing on each face is equal.
This is very similar to the "3-sided coin" problem which aims at finding the thickness for which a coin has probability 1/3 of landing on its edge (Numberphile has a good video on this). In practice, it seems the answer may depend on the surface on which it's thrown. The only truly fair dice which conclusively do not depend on real-world conditions must have only identical faces, and unfortunately not all numbers of faces can produce this (for instance, there is no heptahedron with seven identical faces).
