Counting gluings of octahedra

Understand

Three--dimensional colored triangulations are gluings of tetrahedra whose faces carry the colors 0, 1, 2, 3 and in which the attaching maps between tetrahedra are defined using the colors.

• This framework makes it possible to generalize the notion of two--dimensional $2p$--angulations to three dimensions in a way which is suitable for combinatorics and enumeration.
• In particular, universality classes of three--dimensional triangulations can be investigated within this framework.
• Here we study colored triangulations obtained by gluing octahedra.