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