Abstract
Suppose Pn is a regular n-gon in ℝ2. An embedding f : Pn ↪ ℝ3 is called an α-regular stick knot provided the image of each side of Pn under f is a line segment of length 1 and any two consecutive line segments meet at an angle of α. The main result of this paper proves the existence of α-regular stick unknots for odd n ≥ 7 with α in the range [Formula: see text]. All knots constructed will have trivial knot type, and we will show that any non-trivial α-regular stick knot must have [Formula: see text].
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