3x5x5 (Cubic)Not a bandaged 6x6x6 but a built from scratch cuboid.
Big KahunaThe first fully functional faceturning rhombic triacontahedron.
CelticubeAlso 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.
Compound CubesA hybrid puzzle which combines two axis systems and has a perfectly fitting shape.
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
EyeSkewbA puzzle with 4 axis and many ways to interpret it.
Fang-10An edge-turning pentagonal dipyramid. A puzzle that allows only jumbling moves.