A well lubed 4x4x4 cube is still relatively easy to physically
manipulate. As der Mouse suggests, it is arguably the largest
interesting cube from a solver's point of view.

Probably true; it's the largest cube that actually offers new
challenges. However, bigger cubes are better in that they offer more
variety for making pretty patterns. :-)

Once one starts actually twisting with a 5x5x5 cube, the physical
problems become more severe, e.g. the stickers come off easier,
turning the slice you want to is more of a challenge, etc.

This is interesting, because it's almost exactly the opposite of my
experience.

The problem seems to be the difference between the internal
mechanisms of the odd- and even- ordered cubes.

This brings up an interesting point. Perhaps it would be possible to
build a 4-Cube that was internally a 5-Cube but for which the middle
slice was not actually visible on the surface? Or a 2-Cube that's
internally a 3-Cube? I wonder if it might make for smoother-turning
cubes.

[O]f the four 4X's I've owned, only one was really useable; two were
so stiff they were very difficult to turn (even with lubrication) and
one was so loose that it never lasted more than about 20 minutes
before dissolving into a pile of cubelets [...].

I have owned only one 4-Cube, and it's been long enough since I knew
where it was that I don't recall how easy it was to turn. I now have
two 3-Cubes and a 5-Cube. One of the 3-Cubes is a joy to turn; it's
lubed enough that it turns readily and easily, even when the turn has a
good deal of skew to correct, but it's not so loose that it turns when
I don't want it to. (The other 3-Cube is (a) missing one center cubie
face and (b) much more difficult to turn.) The 5-Cube (one of the
recent Ishi Press cubes, btw) is mechanically quite good, though the
orange stickers did tend to come off (no other color did, and contact
cement worked just fine for putting them back on). Not as good as my
good 3-Cube, though.

I've wondered whether it would be possible to build higher-order cubes.
The corners of the 5-Cube still catch by a respectable amount as the
face turns, but by little enough that it makes me wonder if the 6-Cube
or 7-Cube is actually feasible. (Oh, for a really good
force-reflecting dataglove...then such a thing could be done virtually
with no problem at all!)

der Mouse

mouse@collatz.mcrcim.mcgill.edu