Inequalities for two simplices (Q1583950)

The authors establish inequalities involving two \(n\)-dimensional simplices which combine edge-lengths and altitudes of one simplex with distances from an interior point \(P\) to the facets of the second simplex. For the cases of equalities the first simplices turn out to be regular ones, and for the second simplices either \(P\) coincides with the incenter, or the incenter coincides with the centroid. As consequences, further inequalities for one simplex are obtained, again yielding characterizations of the regular case.