All Polytopes Are Quotients, and Isomorphic Polytopes Are Quotients by Conjugate Subgroups |
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| Authors: | M I Hartley |
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| Institution: | (1) University of Western Australia, Nedlands, WA 6907, Australia hartley@maths.uwa.edu.au, AU;(2) Current Address: Sepang Institute of Technology, Level 5, Klang Parade, 2112 Jalan Meru, 41050 Klang, Selangor Darul Ehsan, Malaysia. hartleym@sit.edu.my., MY |
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| Abstract: | In this paper it is shown that any (abstract) polytope is a quotient of a regular polytope by some subgroup N of the automorphism group W of , and also that isomorphic polytopes are quotients of by conjugate subgroups of W . This extends work published in 1980 by Kato, who proved these results for a restricted class of polytopes which he called
``regular'. The methods used here are more elementary, and treat the problem in a purely nongeometric manner.
Received January 27, 1997, and in revised form October 1, 1997. |
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