I do have a well defined purpose in mind to generate orthogonal projections of n dimensional uniform polytopes into k space maximizing the distance between the image of any j facet and that of any non incident k 1 j facet Nearly all of the higher polytope images in Wikipedia are aligned for maximum symmetry instead This means or at least can be approximated by excluding some bounded pieces of the Grassmannian and finding the points furthest from the excluded pieces A tractable mental image of the space that contains the exclusions would help After another look at operator norm I have a slightly better idea of the shape of my problem just enough to see a flaw in the most obvious approach and not enough to see a practical way around the flaw