I don't have a Mozaika, so I'm not sure whether this idea will work.

First, you turn the Mozaika into what I call an "8-Mozaika". A normal Mozaika has 12 tiles around an equator. An 8-Mozaika has only 8 tiles around an equator. This modification is simply removing 12 tiles--one from each "edge pair"--and praying that half-tile shaped gaps remain between neighboring tiles.

Second, you glue 1.5x1.5 sized square faces onto each tile so they really do maintain the proper spacing.

Third, you add on cubie corners to each corner and 45-45-90 prism wedges onto each of the 12 "edge" tiles.

The result is a slightly distorted 3x3x3 Rubik's cube which happens to allow 45 degree equator rotations.

You could play with this cube all day just like a normal Rubik's cube and never accidentally discover its secret ability to "morph" into non-cubical shapes! In normal cube play, you're used to making an equator rotation by first rotating one side (either 90 degrees or 180 degrees) and then rotating the other side. You won't just accidentally have an equator rotated 45 degrees.

Well, that sounds like a good idea too. You're just full of them.

Have you tried this? I don't have a Mozaika yet, but buying one to try this sounds tempting.

Sandy