Null-strut calculus. I. Kinematics

This paper describes the kinematics of null-strut calculus—a 3+1 Regge calculus approach to general relativity. We show how to model the geometry of spacetime with simplicial spacelike three-geometries (TET's) linked to "earlier" and "later" momentumlike lattice surfaces (TET*) entirely by light rays or "null struts." These three-layered lattice spacetime geometries are defined and analyzed using combinatorial formulas for the structure of polytopes. The following paper in this series describes how these three-layered spacetime lattices are used to model spacetimes in full conformity with Einstein's theory of gravity.