Three Puzzles - Tiling a 3x3x3 Cube

thingiverse

A Cubical Tiling of 27 Sub-Cubes Achieved with Limited Pieces The tiling procedure for a cube (3x3x3) made up of 27 sub-cubes can be simplified by placing restrictions on the process, resulting in a straightforward solution with few possible outcomes. In this instance, the tiling is restricted to four specific pieces: three identical pieces composed of seven sub-cubes and one piece made up of six sub-cubes. Through an extensive search, seven sets of three identical pieces consisting of seven sub-cubes were discovered, which can be combined with a single piece made of six sub-cubes to perfectly tile the 3x3x3 cube. It's worth noting that multiple six-subcube pieces can be used in conjunction with certain sets of seven sub-cube pieces, leading to a total of 23 unique combinations that satisfy the tiling requirements. Five STL files are included as part of this submission: The first file, "seven_set.stl," contains one of the distinct sets of three identical pieces composed of seven sub-cubes.