polypodium with a double l

There is a real English rule pulling on this spelling. A short vowel followed by a single consonant usually wants that consonant doubled, which is why we have jolly, folly and volley rather than joly, foly and voley. The word looks like it should follow suit. It does not, because poly is a prefix rather than an English word, and prefixes keep their own shape however the syllables around them fall.

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