Background (lino cuts by Henk van der Vorst)

n-simplex S: convex hull of n + 1 affinely independent points in Rn facet Fv opposite a vertex v of S: convex hull of the n vertices of S other than v dihedral angle γ between two facets F and G of S: pi minus the angle between outward normals to F and G An n-simplex has (n2) dihedral angles 02. Acute, right, and obtuse dihedral angles Each facet makes at least one acute angle with another face