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.
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.