Stick number of Trefoil So it is well know that the stick number (i.e. the minimum number that is need to make a knot out of -not necessarily of the same length- sticks) of every non-trivial knot is above six, with only the trefoil ataining the minimum. But it seems that I have found a counter example. ![enter image description here]( Since we can trecolor it the knot is not trivial and also since it has exactly 3 crossings it is the trefoil. What am I missing ?

You seem to be dealing with an invariant that is similar to but not quite the stick number. If I understand your invariant, you are taking all knot diagrams made of only straight lines and finding the minimum number of straight lines in any such diagram. Your example shows that for the trefoil this invariant is at most $5$.

The stick number, on the other hand, has to do with piecewise linear embeddings of the circle into 3D space, and it is the minimum number of line segments in any such parameterization. Your example does not correspond to a piecewise linear embedding in 3D. It has a sort of Penrose triangle paradox if you try to lift it to 3D.