Meffert's Pocket Cube
The unpredictable shape changes are produced by a concept called ’bandaging’, combined with a shape transformation technique often referred to as ’modding’. The puzzle is actually a 3x3x3 cube with pieces fused (’bandaged’) together and extended to produce a simpler looking puzzle.
There are several different solved states that are all indistinguishable from one another, meaning there is more than one solution.
The puzzle is off center for turning.