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

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

Long dice and teetotums can, in principle, be made with any number of faces, including odd numbers. Long dice are based on the infinite set of 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.