The mapping from the regular solids to $Z_5$ given by the number of sides in the solid mod 5, interestingly, is a bijection. Any geometers or algebraists know if there is a significant reason for this? I mean, the fact that it is a possibility (i.e. that there are exactly 5 regular solids) is a well known proof, but why is this particular mapping bijective? Just seems too much of a coincidence.