We found one dictionary that defines the word symmetrophile:

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1. symmetrophile: Wiktionary

Definitions from Wiktionary (symmetrophile) ▸ noun:  A lover of symmetry. ▸ Words similar to symmetrophile ▸ Usage examples for symmetrophile ▸ Idioms related to symmetrophile ▸ Wikipedia articles (New!) ▸ Popular adjectives describing symmetrophile ▸ Words that often appear near symmetrophile ▸ Rhymes of symmetrophile ▸ Invented words related to symmetrophile