Friday, May 10, 2013

The simplest corrugated kagome (korgome) basket

The simplest bipartite cubic map is the theta graph embedded in the sphere, so its dual, a triangle embedded in the sphere, is the simplest chess-colorable triangulation. The kagome weaving of this two-sided triangle yields the simplest corrugated kagome basket (or korgome for short.) The weave pattern is strictly kagome, but the weavers can be full-width and cross at 90-degrees because alternate triangles are folded inward. The corrugation also adds stiffness.

Marked up and pre-creased weaver for the simplest corrugated kagome basket.

Starting the weaving.

A tuck-through move.

Taping up the one splice. The basket is still convex at this point.

The convex face of the basket after "popping in."

The convex face of the simplest korgome basket.

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