Author: Brigitte Servatius and Herman Servatius
Reference: Discrete Math. 149, 223--232, (1996).
Selected Figures:
This is a self-dual graph with no $2$-isomorphic self-dual map.
This graphs is drawn on an unfolded cube. The best way to view is to print
it out, coloring the edges by joing solid vertices red and
edges joing hollow vertices blue. Then cut it out and fold it into
a cube.
Abstract: We consider the three forms of self-duality that can be exhibited by a planar graph $G$, map self-duality, graph self-duality and matroid self-duality. We show how these concepts are related with each other and with the connectivity of $G$. We use the geometry of self-dual polyhedra together with the structure of the cycle matroid to construct all self-dual graphs.