3*3*3 6-Piece Diabolical cube

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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.[1][2] 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.

https://en.wikipedia.org/wiki/Diabolical_cube

It shows a puzzle called the Diabolical Cube, which is rather a misnomer as it is one of the easier puzzles of its type. The six pieces, illustrated in Fig. 48, assemble into a 3 x 3 x 3 cube 13 different ways. Since all of the pieces in this puzzle have reflexive symmetry, it necessarily follows that every solution must either be self-reflexive or be one of a reflexive pair. It is customary not to count these reflexive pairs as two different solutions. This particular version of what has now become a very common type of puzzle is unusual in that all of the pieces are flat and contain different numbers of cubes increasing in arithmetic progression.

The Puzzling World, Fig.48

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