Cubic Rubik

Originally, the tangle puzzles are intended to fill a square board.
Gordon Kattau inspired me to cover the faces of a cube with the tiles.

Simple cube

The 24 unique tangle pieces can be used to form a 2x2x2 cube.
The solution can be rather easily found by trying, without a computer.

At first sight, my way of unrolling the cube may appear strange; the reason for this is, it is more compact and more symmetrical than the traditional unrolling.

All six faces of the cube are formed with the same blocks of 2x2 tangle pieces.
All eight corners of the cube are formed with the same L-block; all the quarter-circles are oriented around the corners of the cube, thus the figure has 8 'contracted' circles.

Quadruple cubes

When using the unique pieces four times, it is possible to form larger 4x4x4 cubes. There are exactly 6 solutions, shown here.

Rather than using the original alphabetical labels of the tangle pieces, I have identified each piece with a number 01 - 24, each one appearing four times.

Solutions 3,4 and 6 have one axis of symetry marked with a cross, thus the cube is formed of two identical halves;
solutions 1 and 5 have three axis of symetry, thus the cube is formed of four identical 'bicubic' blocks;
solution 2 has no axis of symetry but it is in a certain sense mirror-symetrical.

In the six solutions, the quarter-circles are not always oriented in the same way; thus not all the solutions have the same number of circles: solution 1 has 6 face-circles, 12 edge-circles and 8 contracted corner-circles (the maximum number of circles); solution 2 has only 12 edge-circles; the other solutions have 6 face-circles and 8 contracted circles.

Solutions 3,4,5,6 form a sort of subfamily; for example the 12 tangle pieces of the first L-block around the red corner-circle are exactly the same for these solutions; some of the other L-blocks are the same or are different between the solutions of this family.

Patrick Hahn - (14.12.4) - Homepage - [Puzzles] [Fractals] [Anagrams] [Software] [Humor] [Photos]