# Cuboid Twisty Puzzles

Rubik’s Cubes have shaped the way we think about problems in life, and have demonstrated that most problems and puzzles don’t always have the simplest solution, but they are always solvable. The original Rubik’s Cube received a lot of attention and fame in the 1980s, which led to a mass developed 4x4x4 being marketed under the names Master Cube and Rubik’s Revenge. This eventually led to the Rubik’s Professor 5x5x5 cube, but puzzle designers already had everything they needed to take the twisty puzzle world to a new level – Cuboids.

The world’s first fully functional cuboid transformation was Tony Fisher’s 3x3x4 puzzle, made from a Rubik’s Revenge. This was Tony Fisher’s first of currently 12 fully functional cuboid puzzles, however this one is the most ground-breaking due to its implications on the world of twisty puzzle design, including the methods used by Fisher to create the extra pieces needed to utilize a currently existing mechanism.

## Shapeshifting

The majority of all cuboids are based on existing NxN mechanisms, and are fully functional (this means that each layer on each face functions as normal, and there are no restricted moves). There are several different types of cuboid design that all fall into one of the two categories:

• Shapeshifting Cuboids – Cuboids that can shapeshift (and thus have to be returned to cuboid shape before being solved). Shapeshifting cuboids, by rule, must two or more edge units with different lengths which are either all odd or all even (for example, a 3x3x5 cuboid).
• Non-Shapeshifting Cuboids – Cuboids that cannot shapeshift (all moves in one direction are all half turns, as no quarter turns are permitted). Non-Shapeshifting cuboids do not conform to the above rule.

## Common Cuboid Shapes and Sizes

There are also a number of different cuboid shapes and sizes, some of which have collective groups:

• 2x2xN Cuboids – These cuboids (known as Tower Cuboids) are progressively taller tower-style puzzles that are very simple to solve due to their limited movement (regardless of the above shapeshifting rules, the shapeshift on a tower cuboid is very easy to fix so most the solve is standard).
• 3x3xN Cuboids – Slightly more difficult alternatives to the tower cuboids, the 3x3xN cuboids are similar in shape and design except their two end faces are 3x3, not 2x2. Some popular examples include the 3x3x2 Domino Cube and 3x3x4.
• NxNx1 Floppy Cuboids – These puzzles are only one layer thick, so are usually quite simple to solve.
• Non-Proportional Cuboids – Most cuboids are proportional i.e. their pieces are all the same size (like on standard NxNxN cubes), however non-proportional techniques are usually used to make much larger cuboids in a small amount of space (such as Oskar van Deventer’s 3x3x27 “Pancake Cube”, which is no larger than a standard Rubik’s Cube (picture each layer cut into 9 different layers).

Pancake Cube available at shapeways.com

The largest cuboid ever to be produced is the Traiphum's 10x10x8. Most larger puzzles tend to have curved pieces that make the it not necessarily rectangular, but almost as if the insides were bulging outwards. This is a fairly common design, along with the strangely shaped pieces, for two reasons:

1. Its stability. The different shaped pieces help make the puzzle more stable in general, and they also allow different, larger cores to be used to construct them (this is why the outward bulge looks as though it’s making room for a larger, more cylindrical centre).
2. The looks. These types of cuboids look a lot more professional and well-designed than entirely proportional blocky shapes that usually make up the simpler, smaller cuboids.