On the combinatorial structure of 0/1-matrices representing nonobtuse simplices

A 0/1-simplex is the convex hull of n+1 affinely independent vertices of the unit n-cube In. It is nonobtuse if none of its dihedral angles is obtuse, and acute if additionally none of them is right. Acute 0/1-simplices in In can be represented by 0/1-matrices P of size n × n whose Gramians G = P⊤P have an inverse that is strictly diagonally dominant, with negative off-diagonal entries.