Designing paths for box shapes using a Rubik’s Snake

Abstract

A Rubik’s Snake is a toy that was invented over 40 years ago together with the more famous Rubik’s Cube. It starts with a straight ruler and could be twisted into many interesting shapes. One important type of shapes is a box shape. Many complicated shapes can be constructed as a combination of box shapes. Therefore it is a fundamental problem to study the box shape. We constructed a path for a general box shape and derived a counting formula. Some other properties and application were also discussed.

Torus knot designs using a Rubik’s snake

“…In Hou S, et al, 11 several theorems about palindromic, periodic and Mo ¨bius Rubik's snakes were proved. In, Hou S, et al, 12 the design for general box shapes using a Rubik's snake was presented with a counting formula derived.…”

Shortest paths of Rubik’s snake composite knots up to 8 crossings

“…In, 14 theorems about palindromic, periodic and Möbius Rubik's snakes were proved. In, 15 a general strategy for designing box shapes using a Rubik's snake was presented and a counting formula was derived. Knot theory 16 is an interesting research area in mathematics that drew a lot of attention.…”