In trying to deeply undestand Grip Theory, particularly for Complex Puzzles, I was wondering about lowering the number of grips, therefore reducing the number of pieces.
The idea that crossed my mind was to try with a Hemicube, a projective polyhedron with 3 faces.
The code is in no way elegant, but it works.

The keys "J", "K", "L" correspond to U, L and R grip respectively (clockwise and anti-clockwise turns are indistinguishable).
Press "R" to scramble the puzzle and "Q" to reset the puzzle.

It's pretty easy to find 1 or 2 move scrambles, I didn't remove them.

Download script and open with Python.
Prerequisite packages are itertools, pygame, sys, math and random.