6 Hyperbolic Geometry 31 6.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 6.2 Ideal Tetrahedra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 6.3 Volume of Ideal Hyperbolic Tetrahedra . . . . . . . . . . . . . . . . . . . . . . . . . . 37 6.4 Hyperbolic Manifolds . . . . . . . . . . . . . . . . . . . . . . . . ....

A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a ...