From teaching experience. XVII. Borders and Curie’s limit groups

When closing a finite linear ornament into a ring, translation along a straight line turns into rotation around a finite-order symmetry axis. A natural analogy between the symmetry groups of crystallographic borders and Curie’s limit symmetry groups with one ∞ axis arises on an endless ring. But the former are seven and the latter are five. Another two are isolated in the paper from the limit groups ∞/m of rotating and ∞/mm of common cylinders. Thereby a mutually unambiguous correspondence has been achieved. The example is recommended for consideration in the university course of crystallography on the topics «Symmetry groups of borders» and «Curie’s limit groups».