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
Pantriagonal magic cube Pantriagonal magic cube A pantriagonal magic cube is a magic cube where all 4"m" pantriagonals sum correctly. There are 4 one-segment, 12("m" − 1) two-segment, and 4("m" − 2)("m" − 1) three-segment pantriagonals. This class of magic cubes may contain some simple magic squares and/or pandiagonal magic squares, but not enough to satisfy any other classifications. The constant for magic cubes is "S" = "m"("m" + 1)/2. A proper pantriagonal magic cube has 7"m" lines summing correctly. It contains "no" magic squares. Order 4 is the smallest pantriagonal magic cube possible. A pantriagonal magic cube is the 3-dimensional equivalent of