Patent ID: 9720881
Date: 2017-08-01
CPC Classifications: E04B,G06F,G09B

Claim:
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.