In zero energy ontology (ZEO) lattices in the 3-D hyperbolic manifold defined by H³ (t²-x²-y²-z²=a²) (and known as hyperbolic space to distinguish it from other hyperbolic manifolds emerge naturally. The interpretation of H³ as a cosmic time=constant slice of space-time of sub-critical Robertson-Walker cosmology (giving future light-cone of M⁴ at the limit of vanishing mass density) is relevant now. ZEO leads to an argument stating that once the position of the "lower" tip of causal diamond (CD) is fixed and defined as origin, the position of the "upper" tip located at H³ is quantized so that it corresponds to a point of a lattice H³/G, where G is discrete subgroup of SL(2,C) (so called Kleinian group). There is evidence for the quantization of cosmic redshifts: a possible interpretation is in terms of hyperbolic lattice structures assignable to dark matter and energy. Quantum coherence in cosmological scales could be in question. This inspires several questions. How does the crystallography in H³ relate to the standard crystallography in Eucdlidian 3-space E³? Are there general results about tesselations H³? What about hyperbolic counterparts of quasicrystals? In this article standard facts are summarized and some of these questions are briefly discussed.