3x5x5 (Cubic)Not a bandaged 6x6x6 but a built from scratch cuboid.
Big KahunaThe first fully functional faceturning rhombic triacontahedron.
Bump GigaminxThe concept of the Bump Cube (aka Mirror Blocks) adapated to a Gigaminx.
Celtic CubeAlso named "cubic face-turning deltoidal icositetrahedron"
ComboctahedronA hybrid puzzle. It looks like the face-turning octahedron and the magic octahedron but allows the moves from both puzzles.
Cube 3-compoundA hybrid puzzle which combines two axis systems and has a perfectly fitting shape.
DeFTIA Deeper Face-Turning Icosahedron. The short form of this gives the puzzle its name.
Dino StarminxA hybrid puzzle which looks like the Dino dodecahedron or the starminx. It combines the types of turns from both preceeding puzzles.
Eitan's NebulaHigher order face-turning icosahedron. a.k.a. Master Eitan's Star - a.k.a. Master FTI
Eye SkewbA puzzle with 4 axis and many ways to interpret it.