Perfect solids
Perfect solids
A solid is a compact convex subset B of En. Two solids B and C are symmetry equivalent if the actions of their symmetry groups G(B) and G(C) on their face-lattices FB and FC, respectively, are equivalent. If B is similar to C whenever B is symmetry equivalent to C, then we say that B is perfect.
The aim of this thesis is to give a contribution to the problem of classifying all perfect solids. A construction for vertex-regular solids is given, based on the adjoint action of a compact semisimple Lie group on its Lie algebra, and a relation between these solids and perfect Wythoffian polytopes is discussed.
University of Southampton
Pinto, Maria do Rosário
0a7e9be9-0957-4173-8b73-e460dcffdfe9
1992
Pinto, Maria do Rosário
0a7e9be9-0957-4173-8b73-e460dcffdfe9
Pinto, Maria do Rosário
(1992)
Perfect solids.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
A solid is a compact convex subset B of En. Two solids B and C are symmetry equivalent if the actions of their symmetry groups G(B) and G(C) on their face-lattices FB and FC, respectively, are equivalent. If B is similar to C whenever B is symmetry equivalent to C, then we say that B is perfect.
The aim of this thesis is to give a contribution to the problem of classifying all perfect solids. A construction for vertex-regular solids is given, based on the adjoint action of a compact semisimple Lie group on its Lie algebra, and a relation between these solids and perfect Wythoffian polytopes is discussed.
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Published date: 1992
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Local EPrints ID: 462203
URI: http://eprints.soton.ac.uk/id/eprint/462203
PURE UUID: e91e7391-ad4c-4209-bd09-0f2acb601dd6
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Date deposited: 04 Jul 2022 19:03
Last modified: 04 Jul 2022 19:03
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Author:
Maria do Rosário Pinto
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