Topological surfaces as gridded surfaces in geometrical spaces

Abstract

In this paper we study topological surfaces as gridded surfaces in the 2-dimensional scaffolding of cubic honeycombs in Euclidean and hyperbolic spaces.

It is indeed possible to embed the tree of life in the 2-skeleton. Every (conected) orientable surface(with an arbitrary space of ends)can be embedded into the 2-skeleton of the cubulation of ${\mathbb{R}}^3$