Reorienting regular n-gons

Joseph A Gallian, Charles A. Marttila

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Imagine that randomly oriented objects in the shape of a regular n-sided polygon are moving on a conveyor. Our aim is to specify sequences composed of two different rigid motions which, when performed on these objects, will reposition them in all possible ways. We call such sequences facing sequences. (Expressed in group theoretical terms, a facing sequence in a group G is a sequence of elements a1, a2, ..., an from G such that G={e, a1, a1a2, ..., a1a2 ... an}). In this paper we classify various kinds of facing sequences and determine some of their properties. The arguments are group theoretical and combinatorial in nature.

Original languageEnglish (US)
Pages (from-to)97-103
Number of pages7
JournalAequationes Mathematicae
Issue number1
StatePublished - Dec 1980


  • AMS (1970) subject classification: Primary 05A15, 20F05


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