For instance, the triangulations of regular polygons (with size given by the number of sides of the polygon, and a fixed choice of polygon to triangulate for each size) and the set of unrooted binary plane trees (up to graph isomorphism, with a fixed ordering of the leaves, and with size given by the number of leaves) are both counted by the Catalan numbers, so they form isomorphic combinatorial classes.
polygon | triangulation | Delaunay triangulation | regular polygon | Triangulation station | Triangulation (geometry) | Triangulation | The Polygon, Southampton | Polygon triangulation | polygon (computer graphics) | Polygon | General Polygon Clipper | Delaunay Triangulation | Causal dynamical triangulation |
It is also possible to formulate a version of the point set or polygon triangulation problems in which one is allowed to add Steiner points, extra vertices, in order to reduce the total edge length of the resulting triangulations.