This is a new puzzle form, it is called: 6-Truncated Tetrakis Hexahedron http://dmccooey.com/polyhedra/6TruncatedTetrakisHexahedron2.html
I once made it in the pCubes simulator and have long wanted to make a real puzzle.
there are 32 faces. geometry is close to a regular cube. this is a truncated "Tetrakis Hexahedron".
Pentagonal faces have two jumble-angle : ArcCos(-1/9) and ArcCos(-2/3)
I also unbandaged one part to get even more confusing states