I've been playing around with the 5x5x5 today. After seeing Nathan Wilson post a picture of his 2x5x5 on the Puzzle Photography group on Facebook, I had some revelations. First, it's very easy to implement cuboids where all the dimensions have the same parity [even / odd] by bandaging from the outside in. Failure to bandage from the outside in can result in some weird things that look like cuboids but aren't [for example, this 3x3x5 lookalike
]. Second, to change parity of a single axis, hide [for odd puzzles] or expose [for even puzzles] the middle layer. For 5x5x5, hiding a middle layer can be countered by extensions to help make layers more proportional.
The "easy" cuboids I mentioned above are as follows for the 5x5x5:
Easy 5x5x5 Cuboids.PNG [ 149.1 KiB | Viewed 588 times ]
Below are all cuboids with largest dimension 5, with the layer hiding process explained for each cuboid.
1x1x5 - Picture above
1x2x5 - Bandage like a 1x3x5 and hide the middle layer on the 3 axis
1x3x5 - Picture above
1x4x5 - Bandaged like 1x5x5 and hide a middle layer on the 5 axis
1x5x5 - Picture above
2x2x5 - Bandage like a 3x3x5 and hide a middle layer on both 3 axes
2x3x5 - Bandaged like a 3x3x5 and hide a middle layer on one of the 3 axes
2x4x5 - Bandaged like a 3x5x5 and hide middle layers on the 3 axis and a 5 axis
2x5x5 - Bandage like 3x5x5 and hide the middle layer on the 3 axis
3x3x5 - Picture above
3x4x5 - Bandage like a 3x5x5 and hide a middle layer on a 5 axis
3x5x5 - Picture above
4x4x5 - Hide a middle layer on two axes
4x5x5 - Hide a middle layer on any axis
5x5x5 - Picture above
Unfortunately, I think these ideas need to be fleshed out in greater detail. There are some unintended consequences that I don't currently know how to deal with. In particular, the 4x4x5 and 4x5x5 made in this way would allow 90-degree turns on a 4x5 side, which should not be possible on a true cuboid. Instead, it would function more like Chino's Cubic 4x4x5
[which I happen to own
Can anyone shed some light on this process of hiding / exposing layers?