Shortest paths of Rubik’s snake prime knots with up to 6 crossings and application to roller coaster design

Abstract

A Rubik’s Snake is a toy that was invented over 40 years ago together with the more famous Rubik’s Cube. It can be twisted to many interesting shapes including knots. Four blocks can form a trivial knot. Previously we have studied the shortest paths for Rubik’s Snake prime knots with up to 5 crossings. In this paper we study how many blocks are needed to form prime knots with 6 crossings. There are three different types of such knots. The results are classified using the DT (Dowker-Thistlethwaite) code. We also apply our findings to roller coaster design by using the tube version of the Rubik’s snake.