Why Five Worlds? Plato's Timaeus 55C D

In the Timaeus, Plato says that the hypothesis of there being five worlds casts a reasonable doubt. Neither ancient commentators of Plato nor modern scholars have succeeded in unveiling the meaning of this hypothesis. I propose that five is the number of combinations with which the five platonic solids can be arranged in sets of four, each set making up a world. I discuss the question of whether Plato's mathematical skills made him equal to the task of calculating the correct number of combinations, as well as the possible reasons why he rejected the hypothesis of there being five worlds.