These pages shows all main types of twisty puzzles. Only 5 platonic solids (tetrahedrons, cubes, octahedrons, dodecahedrons and icosahedrons) are shown and only cuts that allow twisting without shape change are shown.
I have classified the main types here by the number of cuts.
First table contains so called deep cut puzzles. They have a single cut in the middle of the cube and thus all of them have only 2 layers.
All cuts can be either on face, corner or edge axes. There are theoretically 15 such puzzles existing (5 types of polyhedrons x 3 types of turning axes).
Only 3 out of 15 deep cut puzzles have not yet been built.
The second table contains puzzles that have one single cut, producing 2 - 3 layers.
Both deep-cut and shallow-cut puzzles are included in this table. Numbers in parenthesis show additional cuts which produce trivial twisting tips. These tips add aesthetic value to the puzzle, but do not add any complexity to solving the puzzle. Therefore these "trivial cuts" are omitted from the cut count.