The triangulations of a surface can be generated by repeated splitting of vertices starting with the irreducible triangulations of the surface.
Algorithms for generating triangulations and for generating irreducible triangulations are described in "Generating irreducible triangulations of surfaces".
Some properties of the irreducible triangulations of S2, N3, and N4 are in "Irreducible triangulations of low genus surfaces".
surftri is a computer
program which generates triangulations of surfaces. It is
extensively on the program plantri.
source for surftri can be downloaded.
Counts of triangulations are also available.
The surftri download above also contains the lists of the
and N2. The lists of
the irreducible triangulations
are larger and can be downloaded separately.
Irreducible triangulations with up to 11 or 12 vertices are
also available for other surfaces.
A map is a simple graph embedded in a surface such that
every face is simply connected. Maps can be obtained from
triangulations by removing edges.
Algorithms for generating maps are described in the preprint "Generating maps on
surfaces". This generation process uses irreducible
maps as described in that paper. surftri has been
modified to generate maps.
Last updated: 30 October 2015
Created by Thom Sulanke ()