Dynamic and/or practical succinct data structures for triangulations
Take a look at the theoretical work of Castelli et al.  and also the latest papers of J. Barbay.

"Luca Castelli Aleardi, Olivier Devillers, Gilles Schaeffer: Succinct Representation of Triangulations with a Boundary. WADS 2005: 134-145"

"Luca Castelli Aleardi, Olivier Devillers, Gilles Schaeffer: Dynamic updates of succinct triangulations. CCCG 2005: 134-137"

"Jérémy Barbay, Luca Castelli Aleardi, Meng He, J. Ian Munro: Succinct Representation of Labeled Graphs. Algorithmica 62(1-2): 224-257 (2012)"

For the implementation side, i would check CGAL and its triangulation data structures.