Pseudo-Polycubes of Order 1..4
If you join 1 through 4 cubes at their faces or edges you get 100 different pieces.
I 3D-printed the pieces, but it's faster to get a computer solution for constructions with
these pseudo-polycubes than to put the pieces together.
Because it's difficult to take a special piece out of the whole set,
I first separated small, planar and symmetric pieces. Then I divided the remaining pieces into groups depending
on the number of edge connections and arranged mirror pieces together. Among the groups I searched for
the computer number of each piece and placed it on a 10x10 board.
Now I could start putting the pieces together due to the given layers. Unfortunately sometimes two or three pieces were wrapped
around each other in the computer solution, so that the real construction failed and I had to begin with a new computer solution.
Click the pictures to see the layers.
You can construct four 4x4x6 boxes, which can be combined to get a square ring or other large boxes.
The 3D-printed pieces are sturdy but not true in size. Therefore the 8x8 square ring shows little gaps
and is a little bit unstable.