orthography - Hyphens in words with prefixes like neo-Nazism


I have a question regarding the use of hyphens in words with certain prefixes. For example,



Neo-Nazism
Neo-Confucianism
Neo-liberal



are words with a hyphen, but



Neoplatonism
Neocolonialism



are words without hyphens. I'm especially confused with neo-Confucianism and neoplatonism: one contains a hyphen and a capital letter and the other doesn't.


Is there a specific rule for hyphens in words with prefixes or is it purely arbitrary?




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