spherical polyhedron S = (V, F ;E): For a 2-connected planar graph GS = (V,ES), drawn without self-intersection on a sphere (or in the plane), we record the vertices as V and the regions as faces F , and rewrite the directed edges E as ordered 4-tuples e = 〈h, i; j, k〉, where the edge from vertex h to vertex i has face j on the right and face k on the left. (The reversed edge −e = 〈i, h; k, j〉 ...