The Geometry of an Equifacetal Simplex

Details The Geometry of an Equifacetal Simplex The Geometry of an Equifacetal Simplex

2004-08-10

arxiv.org/abs/math/0408132v2

Mathematika 52(2005), 31-45

Mathematics

Metric Geometry

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Scientific paper

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 centers. It is conjectured that a simplex with a unique center must be equifacetal. The notion of the combinatorial type of an equifacetal simplex is introduced and analyzed, and all possible combinatorial types of equifacetal simplices are constructed in even dimensions.

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