The center conjecture for equifacetal simplices

An equifacetal simplex, in which all facets are congruent, has a unique center. The center conjecture states that a simplex that has a unique center must be equifacetal. A strong version of the conjecture is proved in dimensions at most six by showing that there is an explicit list of centers, defined for all simplices, whose coinciding implies the simplex is equifacetal. It remains an open problem whether the conjecture is true in dimensions greater than six.Peer Reviewe