Virtual Cubes

Rail Cube

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Rail Cube

In it's initial state the Rail Cube features a single closed rail road track covering all six faces of the cube. The locomotive and five colored waggons (yellow, red, pink, blue, green) are located on the center pieces. The purpose of this cube is to explore alternative networks and to connect the vehicles by using intersections, straight and curved track pieces.

The layout of the Rail Cube was created in 2010 by Stefan Berinde.

Full solutions

Single closed track: Along with the initial state a total of two distinct solutions with a single closed track exist. These solutions are connecting only one of the intersection forks.

Algorithm for the other full solution:
D' F2 U (R2 F')2 D' L' U L' U' R' U2 R D2 U L2 (18 ftm, 24 qtm)

Partial solutions

The amount of partial solutions is very large and can be grouped into:

Single non-looped track: Tracks that connect all vehicles in various orders.

A looped and a non-looped track: Several solutions with loops containing 1, 2, 3 or 4 vehicles while the others remain in a non-looped track (two non-intersecting loops haven't been found).

Two looped and a non-looped track: The loops can contain 1 and 2 or 2 and 2 vehicles while the others remain in a non-looped track.

Connected network of multiple loops: A network using all four intersection forks is still waiting to be discovered.

Incomplete solutions

Full and partial solutions are both using all 54 track pieces. Other solutions are considered to be incomplete solutions.

© Walter Randelshofer. All rights reserved.