Thursday, June 20, 2013

Frequency-1 puck weaving of the tetrahedron

A tetrahedron in frequency-1 puck weaving. The forward corner is an all-outboard vertex. (The tetrahedron is self-dual. Putting cube-corner pyramids on the triangular faces of the dual tetrahedron makes a cube.)

In frequency-1 weaving of the tetrahedron, the diagonal corrugation folds open out to 180 degrees, effectively disappearing. We are left with a set of three composite weavers essentially having only the square folds. These form a cube-like surface (actually a tetrahedron decorated with cube corner pyramids) from three orthogonal, belt-like paths. Two unit weavers overlap to form each belt. The total number of unit weavers used is 4*1.5 = 6.

Within each composite belt, body diagonals of the "cube" connect points of the same type. Therefore, if we start at an all-outboard point we can finish at the body-diagonally opposite corner of the "cube" at another all-outboard point.

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