Trivial knots with arbitrary projection

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Abstract
Let k be a polygonal knot in Euclidean 3-space, p a projection onto a plane. If p;/k is 1:1 except at a finite number of points, which are not vertices of k and at which p/k is 2:1, then p(k) is said to be a regular projection of k this means that p(k) is closed curve with a finite number of double points (“crossings”) which are not points of tangency. Clearly for every polygonal knot there is a plane onto which it can be projected regularly. At each crossing of p(k), the knot k assigns an overcrossing arc and an undercrossing arc of the projection; conversely, if at each crossing we say which arc is an overcrossing, then there is a knot, uniquely determined up to homeomorphism, with this regular projection with the assigned overcrossings.

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