Necessity of half-turn twists in the edgeless case

Determine whether every configuration accessible in the edgeless case using half-turn and quarter-turn basic twists is also accessible using quarter-turn and reverse-quarter-turn twists alone.

Background

For edged cubes, the paper proves that convergent sequences are twist-finite, so every half-turn can be replaced by two quarter-turns without affecting convergence. The analogous replacement property is not established for edgeless cubes, where convergence behaves differently and is not closed under concatenation.