Congruent Hexacubes in Boxes

The hexacubes above are all known to be rectifiable. There are links to most of these.

The hexomino below is rep-n2 for all n and so the corresponding hexacube is rep-n3 for all n.

The next diagram shows three boxes made with a hexacube.

2x4x6, 3x4x4 and 4x5x6 boxes made with a hexacube (shown)

This next construction is a 3 x 5 x 6 box with 15 copies of the hexacube shown. Surprisingly this is the smallest box which can be made with this hexacube and so the hexacube has odd order.

Torsten Sillke has produced a number of packings of a 6x6x6 cube with congruent hexacubes. The first few diagrams show halves or thirds of the cube.

Patrick Hamlyn has shown that the constructions below are minimal.

The 6x12x35 block below is by Helmut Postl