Shortest paths of trefoil knot designs using Rubik’s Snakes

Abstract

A Rubik's Snake is a toy that has been around for more than 40 years. It can be twisted to many interesting shapes. In particular a Rubik's Snake can be twisted to form a knot. The trefoil knot is the simplest non-trivial knot. In this paper we study how many blocks are needed to form a trefoil knot for the original version of the Rubik's Snake with integer multiple of 90 degree rotations for joints. We also study how many blocks are needed to form a trefoil knot using the tube version of the Rubik's Snake.