This is my current collection of owned twisty puzzles. I can solve each of them.
2X2X2
3X3X3
Bandaged Cube
Quantity: 1
The first mass produced bandaged 3x3x3 with only one unbandaged piece.
Toys Tiled Cube
Quantity: 1
This plain tiled cube suffers from the same lack of quality common to all the "Toys" cubes.
Void Cube
Quantity: 1
A 3x3x3 with a hole through the center.
White Cube
Quantity: 1
This 50 mm white plastic cube has painted dots instead of stickers.
4X4X4
CUBE (SHAPE CHANGING)
Bump Cube
Quantity: 1
The Bump Cube is a simple 3x3x3 Rubik's cube, but with an interesting twist. It spawned a whole series of puzzles and created a verb of its own.
Fisher Cube
Quantity: 1
Taking the concept of the Rubik's cube and turning it 45 degrees.
Windmill Cube
Quantity: 1
A 3x3x3 variation built by Katsuhiko Okamoto.
CUBOID
2x2x3 (aka Slim Tower)
Quantity: 1
A formerly custom now mass produced 2x2x3 cuboid, commonly known as the "Slim Tower"
2x3x3
Quantity: 1
Cuboid, made after the original cube craze, first customly from a 3x3x3, then mass produced.
OCTAHEDRON
Trajber's Octahedron
Quantity: 1
Of this 3x3x3-variant only few examples were produced and sold in the eighties.
DODECAHEDRON
Megaminx (1999)
Quantity: 1
This is a newer version of the Megaminx, published by Meffert, with tiles and 12 distinct colours.
FOUR
Mastermorphix
Quantity: 1
A higher-order Pyramorphix. A 3x3x3 transformed into the shape of a tetrahedron.
SPHERE
SIAMESE & FUSED