Cubic Polyhedra

@inproceedings{GoodmanStrauss2002CubicP,
  title={Cubic Polyhedra},
  author={Chaim Goodman-Strauss and John M. Sullivan},
  year={2002}
}
A cubic polyhedron is a polyhedral surface whose edges are exactly all the edges of the cubic lattice. Every such polyhedron is a discrete minimal surface, and it appears many (but not all) of them can be relaxed to smooth minimal surfaces (under an appropriate smoothing flow, keeping their symmetries). Here we give a complete classification of the cubic polyhedra. Among these are five new infinite uniform polyhedra and an uncountable collection of new infinite semiregular polyhedra. We also… 
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