A Rubik’s Snake with General Rotation Angles

Self Cite

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.

Section: Prime Knots With 6 Crossingsmentioning

confidence: 99%

“…In, 12 the tube version of the Rubik's Snake is introduced. The idea is that each block of the Rubik's Snake corresponds to a tube of the same shape.…”

Section: Application To Roller Coaster Designmentioning

confidence: 99%

See 1 more Smart Citation

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

Hou¹,

Su²,

Mufutau³

2022

Self Cite

“…9 General rotation angles are mentioned in 8 and more theoretical work was presented in. 10 On the other hand, 9 has quite some theoretical work but is only concerned with integer multiple of 90 degree rotations. In Hou S, et al, 11 several theorems about palindromic, periodic and Mo ¨bius Rubik's snakes were proved.…”

Section: Introductionmentioning

confidence: 99%

Torus knot designs using a Rubik’s snake

Hou,

2024

Self Cite

“…On the other hand, 11 has quite some theoretical work but is only concerned with integer multiple of 90 degree rotations. In, 12 Rubik's Snakes with general rotation angles were studied with theoretical work presented. In, 13 theorems about palindromic, periodic and Möbius Rubik's Snakes were proved.…”

Section: Introductionmentioning

confidence: 99%

Designing paths for box shapes using a Rubik’s Snake

Hou¹

2022

Self Cite

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.