Any piece which relates to a non-zero volume in all of 3D space (can be infinite volume) created by the cut planes which define the puzzle. Below are some examples. Click on the thumbnails to see animations of the real piece types being counted.

Real pieces found in a Corner Turning Cube

Real pieces found in an Edge Turning Cube

Real pieces found in a Face Turning Dodecahedron

Real pieces found in a Corner Turning Dodecahedron

Real pieces found in an Edge Turning Dodecahedron