Ideal tetrahedra and their duals

          @misc{ scivideos_PIRSA:19110063,
            doi = {10.48660/19110063},
            url = {https://pirsa.org/19110063},
            author = {Meusburger, Catherine},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Ideal tetrahedra and their duals},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2019},
            month = {nov},
            note = {PIRSA:19110063 see, \url{https://scivideos.org/pirsa/19110063}}
          }
          

Abstract

Recently they have been generalized to other 3d homogeneous spaces, namely 3d anti de Sitter space and half-pipe space, a 3d homogeneous space with a degenerate metric.

We show that generalized ideal tetrahedra correspond to dual tetrahedra in 3d Minkowski, de Sitter and anti de Sitter space. They are those geodesic tetrahedra whose faces are all lightlike.

We investigate the geometrical properties of these dual tetrahedra in a unifi ed framework.  We then apply these results to obtain a volume formula for generalised ideal tetrahedra and their duals, in terms of their dihedral angles and their edge lengths.

This is joint work with Dr Carlos Scarinci, KIAS.