Radial level planarity testing and embedding in linear time.
The intersection matrix of a simplicial complex has entries equal to the rank of the intersecction of its facets. We prove that this matrix is enough to define up to isomorphism a triangulation of a surface.
We describe how the simple planar quadrangulations with vertices of degree 3 and 4, whose duals are known as octahedrites, can all be obtained from an elementary family of starting graphs by repeatedly applying two expansion operations. This allows for construction of a linear time generator of all graphs in the class with at most a given order, up to isomorphism.