# Can a trefoil knot be stretched to look like a triangle with three knots at the vertices?

Can a trefoil knot be stretched to look like a triangle with three knots at the vertices, like in the right side of the image below, or is that transformation impossible to happen? If possible, what is the nature of the crossings that has to occur at the three corners of the triangle like figure on the right hand side?

• The trefoil knot is a prime knot, i.e. it cannot be split to 3 (or any number $\geq2$) successive knots Commented Apr 29, 2015 at 18:34
• @user8268. Can you extend on your statement and infer on if the right hand image is possible or not? Thanks again. Am not a topologist! Commented Apr 29, 2015 at 18:38
• see e.g. wikipedia for the definition of prime knots. Trefoil being prime implies that the right hand image is impossible (provided the knots at at least 2 of the 3 vertices of the triangle are nontrivial :) [I'm not a topologist either] Commented Apr 29, 2015 at 19:36
• Thanks! I'd need a microscope to zoom if these vertices are non-trivial :) Commented Apr 30, 2015 at 3:01

$$\boldsymbol{\operatorname{Figure:}} \text{ The Stretchfoil}$$