This puzzle is an old one - often admired - search for O'Beirne's cube to see references. It consists of 6 pieces which form a cube and also five rectangular solids. The cube dimensions are 12x12x12, a volume of 1728 units, the pieces all have 288 unit volumes - 6 x 288 = 1728. The rectangular solids have dimensions of 16x18x6, 16x12x9, 12x24x6. 8x24x9, and 8x18x12.

Three mirror image pairs make the 6 pieces - here the "a" pieces are red, the "b" pieces gray, and the "c" pieces yellow. There is a stepwise relation between the solutions that the coloring makes clear. The pieces are easily and quickly printed. OpenSCAD code that shows the solutions is included.

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The article that introduced the puzzle appeared in the New Scientist - go to google books search page - https://books.google.com/ - type in "new scientist 2 march 1961" and seach within that issue for "560" - the page number - or "o'bernie" - the author. see also https://johnrausch.com/PuzzleWorld/art/art01.htm which contains a number of references. The a,b,c labels come from the above article.

The cube has a center of inversion as do all the rectangular solids; see the images of the faces of the cube below - opposite faces are mirrored.