2004/08/31 by Allan L. Edmonds · 1 citation
Mathematics · #math.MG #msc:52B11 #msc:52B15
published as Mathematika 52(2005), 31-45 · Final revision
arxiv created 2006/10/06 · arxiv updated 2009/12/01
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.