Year: 2025
Type: article
Abstract: 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».
Source: Vestnik of Geosciences
Author: Yuri Voytehovskiy
Institution: Herzen University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4411574236