A fair die is a die whose possible face outcomes have equal probability under a specified rolling experiment. For a die with 
possible face outcomes, each therefore has probability 
(Pegg 2005).
An isohedron provides fairness by symmetry when the rolling experiment and the die's mass distribution respect its face-transitive symmetries. These symmetries interchange any two faces without changing their probabilities, so all face outcomes have equal probability. This is a sufficient symmetry condition, rather than the definition of probabilistic fairness. Unintended manufacturing defects, deliberate changes to the die's shape or mass distribution, or a biased rolling experiment can invalidate the symmetry argument (Pegg 2005).
