Non-discrete Frieze Groups

Canadian mathematical bulletin

Alan F. Beardon¹ 

[1] Centre for Mathematical Sciences , Wilberforce Road , Cambridge CB3 0WB, UK

关键词: frieze groups;    isometry groups;   

DOI  :  10.4153/CMB-2015-071-0

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

The classification of Euclidean frieze groups into seven conjugacyclasses is well known, and many articles on recreational mathematicscontain frieze patterns that illustrate these classes. However,it isonly possible to draw these patterns because the subgroup oftranslations that leave the pattern invariant is (by definition)cyclic, and hence discrete. In this paper we classify the conjugacyclasses of frieze groups that contain a non-discrete subgroup oftranslations, and clearly these groups cannot be representedpictorially in any practical way. In addition, this discussionshedslight on why there are only seven conjugacy classes in the classicalcase.

【 授权许可】

Unknown