Designing paths for box shapes using a Rubik’s Snake

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.