Hi, everyone: I would appreciate any help with the following: I am trying to refresh my knot theory--it's been a while. I am trying to answer the following: 1) Every simple polygonal knot P in R^2 is trivial.: I have tried to actually construct a homeomorphism h:R^3 -->R^3 , with h|_P = S^1 , i.e., the restriction of the automorphism h to the poly. knot P gives us S^1 I actually tried going in the opposite direction by creating a homeo. between a polygonal knot P and S^1 (and seeing if I can extend it to h:R^3 -->R^3 ): find a circle C going through the vertices of P (So that C an P are coplanar) and then smoothly deform P to S^1. But I cannot see how to extend this to an homeo. h:R^3 -->R^3 that restricts to this map. 2) Show there are no knotted quadrilateral nor pentagonal knots. I have no clue here. Any Ideas.?. Thanks.