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Corner-turning cube (layers >= 4)
Compy SkewbA corner-turning hexahedron with four (no more!) logical layers.
DaYan Gem IVThe first mass produced face-turning octahedron with three cuts per axis although it does not have the octahedrons shape.
Dino OctaA face-turning octahedron. Built without CAD before the age of 3D-printing!

Dino SkewbA puzzle which allows the moves of a Dino Cube and a Skewb.
Elite skewbThe first corner-turning hexahedron with 3 cuts per axis.
Elite TetrahedronThe tetrahedral cousin of the Elite Skewb but published earlier.

Fadi CubeA twisty puzzle cube that turns around its corners. It has five layers per throughgoing axes.

Lattice CubeCould be thought of as a Master Dino Cube.
Master Face-Turning OctahedronCorrectly proportional Master (4-layer) Face-Turning Octahedron.

Master Rex CubeA corner-turning hexahedron with 7 types of pieces. All cuts still intersect at the corners.
Mosaic CubeMefferts renamed version of the Fadi cube.
Rex SkewbA combination of Skewb and Rex Cube like the name says.

Royal SkewbA corner-turning hexahedron with four cuts per axis. Despite the other puzzles with these properties the cuts are placed closer to the core.
Royal TetrahedronThe tetrahedral cousin of the Royal Skewb but invented earlier.
Tetrahedral TwinsA stella octangula-shaped puzzle that is like a Master Pyraminx with an additional turning tip added to each face.

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