The Tiling of the Hyperbolic 4D Space by the 120-Cell Is Combinatoric

Abstract

The splitting method, which was defined by the author in [9,10] is at the basis of the notion of combinatoric tilings. As a consequence of this notion, there is a recurrence sequence which allows us to compute the number of tiles which are at a fixed distance from a given tile. A polynomial is attached to the sequence as well as a language which can be used for implementing cellular automata on the tiling. We give here the polynomial and, as a first consequence, the language of the splitting is not regular, as it is the case in the tiling of hyperbolic 3D space by regular dodecahedra which is also combinatoric.