Self-Dual Spherical Grids

  • Jack E. Graver
  • Elizabeth J. Hartung
Keywords: Self-dual plane graphs


Self-dual plane graphs have been studied extensively. C. A. B Smith and W. T. Tutte published A class of self-dual maps in 1950; in 1992, Archdeacon and Richter described a method for constructing all self-dual plane graphs and a second construction was produced by Servatius and Christopher in 1992. Both constructions are inductive.  In this paper, we produce four templates from which all self-dual plane graphs with maximum degree 4 (self-dual spherical grids) can be constructed.  The self-dual spherical grids are further subdivided into 27 basic automorphism classes.  Self-dual spherical grids in the same automorphism class have similar architecture. A smallest example of each class is constructed.
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