Rubik's Snake


A Rubik's Snake is a toy with 24 wedges that are right isosceles triangular prisms. The wedges are connected by spring bolts, so that they can be twisted, but not separated. By being twisted, the Rubik's Snake can be made to resemble a wide variety of objects, animals, or geometric shapes. Its "ball" shape in its packaging is a non-uniform concave rhombicuboctahedron.
The snake was invented by Ernő Rubik, better known as the inventor of the Rubik's Cube.
Rubik's Snake was released during 1981 at the height of the Rubik's Cube craze. According to Ernő Rubik: "The snake is not a problem to be solved; it offers infinite possibilities of combination. It is a tool to test out ideas of shape in space. Speaking theoretically, the number of the snake's combinations is limited. But speaking practically, that number is limitless, and a lifetime is not sufficient to realize all of its possibilities."

Structure

The 24 prisms are aligned in row with an alternating orientation. Each prism can adopt 4 different positions, each with an offset of 90°. Usually the prisms have alternating colors.

Notation

Twisting instructions

The steps needed to make an arbitrary shape or figure can be described in a number of ways.
One common starting configuration is a straight bar with alternating upper and lower prisms, with the rectangular faces facing up and down, and the triangular faces facing towards the player. The 12 lower prisms are numbered 1 through 12 starting from the left, with the left and the right sloping faces of these prisms are labeled L and R respectively. The last of the upper prisms is on the right, so the L face of prism 1 does not have an adjacent prism.
The four possible positions of the adjacent prism on each L and R sloping face are numbered 0, 1, 2 and 3. Numbering is based on always twisting the adjacent prism so it swings towards the player: position 1 turns the adjacent blocks towards them, position 2 makes a 90° turn, and position 3 turns the adjacent block away from the player. Position 0 is the starting position, therefore it is not explicitly noted in step-by-step instructions.
Using these rules, a twist can be simply described as:
  1. Number of the downward-facing prism : 1 to 12
  2. Left or right sloping side of the prism: L or R
  3. Position of the twist: 1, 2 or 3
Example FigureTwisting Instructions
Cat
9R2-9L2-8L2-7R2-6R2-6L2-5L3-4L2-3R2-2R2-2L2
Three Peaks
6R1-6L3-5R2-5L3-4R2-4L1-1R1-3L3-3R2-7L2-7R3-8L1-8R2-9L1-9R2-10L3-12R3-11L1-10R2

Machine processing

The position of the 23 turning areas can also be written directly after each other. Here the positions 0, 1, 2 and 3 are always based on the degrees of twist between the right-hand prisms relative to the left-hand prism, when viewed from the right of the axis of rotation.
However, this notation is impractical for human readers, because it is difficult to determine the order of the twists.

Rather than numbers Albert Fiore uses letters to refer to the direction the second section is turned in relation to the first section: D, L, U, and R. These are listed consecutively rather than numbered, so that a completely straight figure rather than being presumed as a starting point is notated DDDDDDDDDDDDDDDDDDDDDDD.

Mathematical formulation

The number of different shapes of the Rubik's Snake is at most 423 = , i.e. 23 turning areas with 4 positions each. The real number of different shapes is lower, since some configurations are spatially impossible. Berkes Dániel and Jakab Ferenc computed by an exhaustive search that positions are possible when prohibiting prism collisions, or passing through a collision to reach another position; or when mirror images are counted as the one position.