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The Geometry of an Equifacetal Simplex

Part of: Polytopes and polyhedra

Published online by Cambridge University Press:  21 December 2009

Allan L. Edmonds
Allan L. Edmonds
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405. U.S.A. E-mail: edmonds@indiana.edu
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Abstract

Equifacetal simplices, all of whose codimension one faces are congruent to one another, are studied. It is shown that the isometry group of such a simplex acts transitively on its set of vertices and, as an application, equifacetal simplices are shown to have unique centres. It is conjectured that a simplex with a unique centre must be equifacetal. The notion of the combinatorial type of an equifacetal simplex is introduced and analysed, and all possible combinatorial types of equifacetal simplices are constructed in even dimensions.

MSC classification

Secondary: 52B11: $n$-dimensional polytopes
Type
Research Article
Information
Mathematika , Volume 52 , Issue 1-2 , December 2005 , pp. 31 - 45
Copyright
Copyright © University College London 2005

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