Cubic Polyhedra

  title={Cubic Polyhedra},
  author={Chaim Goodman-Strauss and John M. Sullivan},
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… 
The {4, 5} Isogonal Sponges on the Cubic Lattice
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A Survey on Quasiperiodic Topology
  • R. Leo
  • Mathematics
    STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health
  • 2019
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A new algorithm to compute stable discrete minimal surfaces bounded by a number of fixed or free boundary curves in R 3, S 3 and H 3 is presented and an algorithm that, starting from a discrete harmonic map, gives a conjugate harmonic map is presented.
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  • Mathematics
    Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1996
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The Surface Evolver
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The Surface Evolver, Experimental Math
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