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 edgeturning pentagonal dipyramid. A puzzle that allows only jumbling moves.