Three 3D Tiling Puzzles

thingiverse

The target to be built is a block of 64 cubes arranged as an array of 4 levels each containing 16 cubes. A full scale version of the target is provided for teaching and to make the construction of the target clear. The individual cubes are outlined. Note that the target is symmetrical with a center of symmetry and three 4 fold rotation axes. The pieces that build the target are octacubes, eight cubes connected by their faces. See the wikipedia article on polycubes -https://en.wikipedia.org/wiki/Polycube - Eight octacubes are required - a total of 64 cubes. The tiling pieces occur in sets of eight identical pieces. If the pieces were all different the puzzles would be difficult to solve. When all the pieces are the same the puzzles are easier to solve, the solutions have symmetry, and are artistically more appealing. The solutions contain sets of 2 and 4 tiles related by symmetry. If the tiles are printed in sets of four with different colors interesting patterns can be created. The three puzzles have unique tilings. Trays are given which can serve to store the puzzle pieces. They can be used as aids during the solution process as they limit the placement of the tiling pieces; pieces can only be placed inside the boundaries of the trays. Make 8 pieces of octa_7.stl, octa_78.stl and octa_128.stl to create the three puzzles. For a single simple puzzle just print 8 copies of octa_7; an octacube where all the cubes lie on a plane. Solutions are given in How Done.