Equivalent classes of degree sequences for triangulated polyhedra and their convex realization

  • Pascal Honvault Université du Littoral Côte d'Opale, France.


We define an equivalence on the set of all degree sequences of a triangulated polyhedron with a fixed number of vertices and compute them and their cardinal via an algorithm. We also prove that each class is realizable as a convex polyhedron.


A.D. Alexandrov, Convex polyhedra, Springer, 2010.

J. S.L Devadoss, J.O'Rourke, Discrete and computational geometry, Princeton University Press, 2011.

P.Honvault, Combinatorics of triangulated polyhedra, accepted for publication in Journal For Geometry And Graphics, 2018.

S. Negami, Diagonal flips of triangulations on surfaces, a survey. Yokohama Math. J., vol.47, 1999.

D.Rorabaugh, OEIS A253882, 2015.

W. T. Tutte. A census of planar triangulations. Canad. J. Math., 14 :21-38, 1962. 18, 21, 45

K. Wagner, Bemekungen zum Vierfarbenproblem, J. der Deut. Math., Ver. 46, Abt. 1, (1936), 26-32.