Skip to main content
Discussion Paper

The Complex of Maximal Lattice Free Simplices

The simplicial complex K(A) is de&#xfb01;ned to be the collection of simplices, and their proper subsimplices, representing maximal lattice free bodies of the form {x: Ax < b}, with A a &#xfb01;xed (n + 1) × n matrix. The topological space associated with K(A) is shown to be homeomorphic to Rn, and the space obtained by identifying lattice translates of these simplices is homeomorphic to the n-torus.