Crystallography of hyperbolic lattices

Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices

We show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and associated symmetry groups

In crystallography, a lattice is an abstract representation of a crystal structure: it is periodic and infinite, and the real structure can be reconstructed by associating with each lattice point the concrete structural motif (molecule, cluster of ions or of molecules) that it symbolically represents

Body-Centered Cubic Crystal Lattice is also called as “BCC” or “Cubic-I” in a unit cell

A body centered cubic (bcc) unit cell has an atom at each of its corners and also one atom at the centre of its body

The body-Centered cubic crystal lattice has atoms similar to that of the cubic unit cell with an extra atom at the centre