With the exception of 10-sided dice, all standard dice used for D&D are platonic solids: a convex polyhedron where all faces are the same shape and size, all angles and sides are equal, and the same number of faces meet at each vertex. Most editions of the game also use 10-sided dice.
Every edition of Dungeons & Dragons has required the use of 4-sided, 6-sided, 8-sided, 12-sided, and 20-sided dice.