2014/02/26 by Horváth, Ákos G., Lángi, Zsolt
#52A38 #52A40 #52B60 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1402.6496
In this paper we investigate the problem of finding the maximum volume polytopes, inscribed in the unit sphere of the d-dimensional Euclidean space, with a given number of vertices. We solve this problem for polytopes with d+2 vertices in every dimension, and for polytopes with d+3 vertices in odd dimensions. For polytopes with d+3 vertices in even dimensions we give a partial solution.