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The Mathematics of Various Entertaining SubjectsResearch in Recreational Math$
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Jennifer Beineke and Jason Rosenhouse

Print publication date: 2015

Print ISBN-13: 9780691164038

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691164038.001.0001

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Groups Associated to Tetraflexagons

Groups Associated to Tetraflexagons

Chapter:
(p.81) 6 Groups Associated to Tetraflexagons
Source:
The Mathematics of Various Entertaining Subjects
Author(s):

Julie Beier

Carolyn Yackel

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691164038.003.0006

This chapter presents an example of the way groups are associated to flexagons, along with several other groups admitted by the actions of tetraflexagons. These tetraflexagons yield rich group structures that are unexpected from such simple objects. Throughout this chapter, a generators and relations approach is used to determine the appropriate group corresponding to each flexagon. For each example, the chapter presents the structure diagrams, discusses particular choices in mathematizing, compares these choices to the previous literature, and reports the associated group. Each example employs slightly different choices in the generator assignment, which serves to capture different aspects of the physical nature of the flexagon itself.

Keywords:   tetraflexagons, flexagons, group structures, simple objects, generator assignment

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