  We realize Lobachevsky geometry in a simulation lab, by producing a
carbon-based mechanically stable molecular structure, arranged in the shape of
a Beltrami pseudosphere. We find that this structure: i) corresponds to a
non-Euclidean crystallographic group, namely a loxodromic subgroup of SL(2,Z);
ii) has an unavoidable singular boundary, that we fully take into account. Our
approach, substantiated by extensive numerical simulations of Beltrami
pseudospheres of different size, might be applied to other surfaces of constant
negative Gaussian curvature, and points to a general procedure to generate
them. Our results also pave the way to test certain scenarios of the physics of
curved spacetimes.
