ABSTRACT
As ε = +1, 0, or −1, let Y ε n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072386/f0e84800-6123-461d-a9d3-5a5098a93bca/content/eq472.tif"/> stand for the n-sphere, Euclidean n-space, or hyperbolic n-space. The study of regular tessellations of Y ε n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072386/f0e84800-6123-461d-a9d3-5a5098a93bca/content/eq473.tif"/> by convex cells is a classical topic. Such tessellations have been completely classified (e.g., see [2] and [3]). The theory of regular tessellations of the n-sphere is essentially identical with the theory of regular convex polyhedra of dimension n + 1. In the case of hyperbolic space, regular tessellations exist only in dimensions 2, 3, and 4 (cf. [2]).
