POLYGONAL KNOT BY COMPUTATIONAL ORIGAMI

We present computer-assisted methods for constructing polygonal knots with verification. We start from the most basic crossing of a paper tape. The construction and the subsequent verification are performed through the interaction with a software tool called e-origami system (abbreviated to Eos), which we have been developing. We tackle the problems of construction and verification of polygonal knots with a simulated tape, i.e. a computer-modeled sheet of origami paper long enough to make a desired knot. Eos has its own simple programming language with which the users of Eos communicate to perform step-by-step construction, as if a piecework of an origami is made by hand. The challenge is to construct regular polygonal knots with rigor and rigidity. This required a method beyond classical Huzita's fold method. We extended the Eos language of the first-order logic specialized to origami geometry. This enabled a line of development from a regular triangle pre-knot to 2n+1 polygonal knot and arbitrary n-gon knot-like objects.