polypoddium or pollypodium, if one of them has to be right?

The two spellings are the same instinct applied at different points in the word. One doubles the l after the first syllable, one doubles the d after the stressed third. Both are looking for the doubled consonant that English uses to mark a short vowel. This name has no doubled letters at all, front or back, because both of its halves came in from Greek already spelled.

A consonant doubled to mark a stress, the way English words do it.