From teaching experience. XVIII. Table of 27 symmetry species

The article discusses two forms of the table of 27 symmetry species (without cubic syngony): the Li4 axis has its own row, and other inversion axes are forbidden; all possible inversion axes are used. The latter case is particularly interesting when comparing the species of symmetry with smooth geometric interpretations (cones and cylinders) of the limiting Curie symmetry groups. It is proposed to distinguish 14 rather than 7 classes of symmetry. The article discusses their nomenclature with a historical overview. The article teaches the creative assimilation of fundamental results, their derivation, and comprehension in detail. It is intended for teachers, postgraduate students, and students (geologists, geographers, biologists, etc.) studying the basics of crystallography in a geometric variant without group theory and linear algebra. The article is dedicated to Professor A. I. Glazov, the last representative of the E. S. Fedorov — A. K. Boldyrev — I. I. Shafranovsky crystallographic school at the Leningrad Mining Institute (now the Saint Petersburg Mining University), and is accompanied by unique photos from the personal archive of Professor D. P. Grigoriev.