Factory made 4x4x5 Cuboids can be purchased here.
This puzzle took a very long time to make. On hind site I probably should have used a different method. I got there in the end though and I'm reasonably pleased with the results. The puzzle was transformed entirely by hand in 2002 using high impact polystyrene plastic sheet. Movement is smooth and it is very light considering it's large size.
Stickers are standard Rubik's Cube style with red opposite orange, yellow opposite white and green opposite blue.
The puzzle can't change shape since it doesn't obey the cuboid shape changing rule-
"A cuboid is capable of shape changing when ( two or more edge unit lengths are different and odd ) or ( two or more edge unit lengths are different and even ) excluding cuboids with a side of one."
In total I have made eleven fully functional cuboids. They are-
2x2x3 (micro), 2x2x4, 2x2x6, 2x2x7, 2x3x4, 3x3x4 (large), 3x3x4 (medium), 3x3x5, 3x4x4, 4x4x5, 4x4x6, 5x5x6