On Device of Octahedron Dice

In 1978,M.Gardner discovered a pair of weird dice(called Sicherman dice),one of which was labeled on the six faces of one cube with integers 1,2,2,3,3,4 and on the six faces of another cube with integers 1,3,4,5,6,8,then the probability of obtaining any particular sum with this dice is the same as the probability of rolling that sum with ordinary dice.In this paper,we consider the case of the dice made by octahedrons.We prove that there are exactly 4 pairs dice made by regular 8-polyhedrons which have the same rolling probability.