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Symmetric Tessellations on Euclidean Space-Forms

Published online by Cambridge University Press:  20 November 2018

Michael I. Hartley ,
Peter McMullen  and
Egon Schulte
Michael I. Hartley
Affiliation:
Sepang Institute of Technology, 2112 Jalan Meru, 41050 Klang, Selangor Darul Ehsan, Malaysia email: hartleym@sit.edu.my
Peter McMullen
Affiliation:
University College London, Gower Street, London WC1E 6BT, England email: p.mcmullen@ucl.ac.uk
Egon Schulte
Affiliation:
Northeastern University, Boston, MA 02115, USA email: schulte@neu.edu
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Abstract

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It is shown here that, for $n\ge 2$, the $n$-torus is the only $n$-dimensional compact euclidean space-form which can admit a regular or chiral tessellation. Further, such a tessellation can only be chiral if $n\,=\,2$.

Keywords

51M20polyhedra and polytopesregular figuresdivision of space
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 6 , 01 December 1999 , pp. 1230 - 1239
Copyright
Copyright © Canadian Mathematical Society 1999

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