Let me define that a polygon knot means a knot K of which all point belongs to some line segment which is a subset of K.
Let me ask if knot theory has some proof for that:
For all pair ( K1, K2 ) of polygon knots which are R3 ambient isotopic to each other,
some R^3 ambient isotopy H exists such that H takes K1 to K2 and all H( K1, t ) is a polygon knot for all time point t of H.
And if it does, could you give me how to prove it?
If there is some unlear point in my question, let me explain it.