The first mass produced bandaged 3x3x3 with only one unbandaged piece.
6X6X6 & UP
The first mass produced 6x6x6. A six layered cube.
The first 7x7x7. A seven layered cube.
CUBE (SHAPE PRESERVING)
The deepcut corner turning cube.
CUBE (SHAPE CHANGING)
Taking the concept of the Rubik's cube and turning it 45 degrees.
Get back to Square-1
An american based version of the Square-1. It distinguishes itself from the other variants because it was sold in scrambled state.
2x2x3 (aka Slim Tower)
A formerly custom now mass produced 2x2x3 cuboid, commonly known as the "Slim Tower"
A highly customized 4x4x4 cube.
Custom 2x3x3 cuboid, made from a 3x3x3.
A fully functional 3x3x4 by Katsuhiko Okamoto.
A jumbling only puzzle which fills a missing slot in the series of face turning tetragonal trapezohedrons between the Crystal Trap and the jumble Trap.
A mix between the moving hole puzzles and the two-layer UFO puzzles.
SIAMESE & FUSED
Two 2x2x2s fused with one common cubie.
Two 3x3x3's fused together to share a block of dimensions 2x2x2.