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Free Extensions of Chiral Polytopes

Published online by Cambridge University Press:  20 November 2018

Egon Schulte  and
Asia Ivić Weiss
Egon Schulte
Affiliation:
Northeastern University, Boston, Massachusetts 02115, U.S.A.
Asia Ivić Weiss
Affiliation:
York University, North York, Ontario, M3J 1P3
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Abstract

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Abstract polytopes are discrete geometric structures which generalize the classical notion of a convex polytope. Chiral polytopes are those abstract polytopes which have maximal symmetry by rotation, in contrast to the abstract regular polytopes which have maximal symmetry by reflection. Chirality is a fascinating phenomenon which does not occur in the classical theory. The paper proves the following general extension result for chiral polytopes. If 𝒦 is a chiral polytope with regular facets 𝓕 then among all chiral polytopes with facets 𝒦 there is a universal such polytope 𝓟, whose group is a certain amalgamated product of the groups of 𝒦 and 𝓕. Finite extensions are also discussed.

Keywords

51M2052A25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 3 , 01 June 1995 , pp. 641 - 654
Copyright
Copyright © Canadian Mathematical Society 1995

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