  We extend previously known two-dimensional multiplication tiling systems that
simulate multiplication by two natural numbers $p$ and $q$ in base $pq$ to
higher dimensional multiplication tessellation systems. We develop the theory
of these systems and link different multiplication tessellation systems with
each other via macrotile operations that glue cubes in one tessellation system
into larger cubes of another tessellation system. The macrotile operations
yield topological conjugacies and factor maps between cellular automata
performing multiplication by positive numbers in various bases.
