The word "cylindraxile" is a neologism, meaning it is a newly invented word. Its spelling can be explained using the International Phonetic Alphabet (IPA). "Cylindra" is pronounced as /səˈlɪndrə/, which means it has an "s" sound followed by a short "i" sound and "nd" sound. "Xile" is pronounced as /zaɪl/, having a "z" sound, followed by a long "i" sound and "l" sound. Together, "cylindraxile" is pronounced as /səˈlɪndrəzaɪl/, emphasizing the separate sounds and showing how it can be spelled.
Axis-cylinder.
A practical medical dictionary. By Stedman, Thomas Lathrop. Published 1920.