4 Corners RotatedA 3x3x3 truncated to give it the shape with an unusual symmetry group.
5x5x5 Diamond CubeA 5x5x5 truncated into a hexagonal dipyramid and then further truncated.
AlphaminxThe first puzzle in a series of Truncated Kleetopes -- this version is a Truncated Triakis Tetrahedron.
Bowtie's CousinA truncated ultimate skewb. The cuts placed on a different set of edges.
Capsule CubeAn elongated rhombicuboctahedron. Or a shape variant of the extended-only 3x3x5.
CirqueminxA megaminx truncated into something barrel-like.
DaYan Gem VIIA mass produced hybrid puzzle which combines face turning and edge turning hexahedron in a solid with 16 sides.