From teaching experience. II. Main theorem of crystallography

The article is devoted to the main theorem of classic crystallography - on the impossibility of n -fold axes of symmetry with n = 5 and n > 6. It is fundamental in the natural sciences, sharply separating mineral and biological structures. The proofs of the theorem in many academic monographs and university textbooks over the past 170 years are considered. Attention is paid to the methodological nuances of proofs of the theorem.