The generalized tilt formula

A convex hull construction in Minkowski space defines a canonical cell decomposition for a cusped hyperbolicn-manifold. An algorithm to compute the canonical cell decomposition uses the concept of the ‘tilt’ of ann-simplex relative to each of its (n−1)-dimensional faces. An essential tool for computing tilts is the tilt theorem. The tilt theorem was previously known only in dimensionsn≤3, and the proof was needlessly complicated. Here we offer a new, simplified proof which applies in all dimensions. We also offer a second geometric interpretation of the tilt.