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CONVEX EQUILATERAL POLYHEDRA WITH POLYHEDRAL SYMMETRY

  • US 20150037766A1
  • Filed: 07/29/2014
  • Published: 02/05/2015
  • Est. Priority Date: 08/02/2013
  • Status: Active Grant
First Claim
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1. A method for designing a convex equilateral cage structure comprising:

  • selecting a Goldberg triangle comprising an equilateral triangle having three vertices that are each positioned on a center of a hexagon in a hexagonal tiling such that the equilateral triangle overlies a plurality of vertices from the hexagonal tiling, wherein the Goldberg triangle further comprises the plurality of vertices and each line segment connecting any two of the plurality of vertices;

    transferring the Goldberg triangle to each of the twenty faces of an icosahedron;

    adding connecting line segments that connect corresponding vertices across adjacent Goldberg triangles such that the Goldberg triangle line segments and the connecting line segments define a non-polyhedral cage, wherein the non-polyhedral cage comprises only trivalent vertices; and

    transforming the non-polyhedral cage such that the transformed cage comprises a plurality of hexagons and a plurality of pentagons, and the transformed cage is equilateral and convex.

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