Diabolical cube Diabolical cube The diabolical cube is a three-dimensional dissection puzzle consisting of six polycubes (shapes formed by gluing cubes together face to face) that can be assembled together to form a single 3 × 3 × 3 cube. The six pieces are: one dicube, one tricube, one tetracube, one pentacube, one hexacube and one heptacube, that is, polycubes of 2, 3, 4, 5, 6 and 7 cubes. There are many similar variations of this type of puzzle, including the Soma cube and the Slothouber–Graatsma puzzle, two other dissections of a 3 × 3 × 3 cube into polycubes which use
Floppy Cube 4); this means they can now be permutated in 12!/(12-4)! different ways. The corners still cannot be flipped; their orientation continues to be fully dependent on their position. All of these positions are attainable: there is no parity constraint, regardless of whether the edge pieces can twist on their own or not. The full number is therefore: This number is significantly larger than the number of combinations on the Floppy Cube. The God's Number for this puzzle is also considerably larger than that of the Floppy Cube: 13 (when edges can twist on their own) or 15 (when they cannot).