'Pulchraphilia' or 'Pulchriphilia' or 'Pulchrophilia'? Does anybody know what the spelling of such a word would be? Should I take the cue from the spelling of pulchritude and use an i, or is an a correct?
Calophilia is properly formed, from Greek kalos "beautiful" and phil- "like/love". But Greek has the odd habit of often creating compound nouns with the minor element (here the substantivised adjective) at the end, which is not normal in Latin or English, as in philanthropy, misogyny or hippopotamus. The word philocaly exists in English, and it exemplifies this little Greek oddity. The word philokalia already existed in Ancient Greek, "love of the beautiful". So it has an impeccable pedigree. All this makes philocaly caliston ("most beautiful") in the eyes of philocalists and pedants alike.
If it is necessary to use the Latin root pulchr-, then it would be pulchriphilia. But the Romans were very unlikely to create compound nouns like this; they normally just used two words, as in amor pulchri "love of the beautiful". Secondly, hybrid Graeco-Latin compounds are generally not preferred.
P.S. See also this question: Is there a word that means “to hate beauty”?.
(P.P.S. I apologize for the grumpiness of some of my colleagues. That's just what this site is known for: it's not you.)