The most successful method to date for finding lower bounds on the number of simplices needed to triangulate a given polytope P involves optimizing a linear functional over the associated Universal Polytope U(P). However, as the dimension of P grows, these linear programs become increasingly difficult to formulate and solve. Here we present a method to algorithmically construct the quotient of U(P) by the symmetry group Aut(P) of P, which leads to dramatic reductions in the size of the linear program. We compare the power of our approach with older computations by Orden and Santos, indicate the influence of the combinatorial complexity barrier on these computations, and sketch some future applications.

Peer Reviewed