English

The Geometry of an Equifacetal Simplex

Metric Geometry 2007-05-23 v2

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 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.

Keywords

Cite

@article{arxiv.math/0408132,
  title  = {The Geometry of an Equifacetal Simplex},
  author = {Allan L. Edmonds},
  journal= {arXiv preprint arXiv:math/0408132},
  year   = {2007}
}

Comments

Final revision

R2 v1 2026-07-22T17:08:38.968Z