Holey OctahedronA void Trajber's Octahedron. Rather than having holes at the tips, this one has holes in the faces.
Hybrid OctahedronAn octahedron with two cuts per corner turning axis and two cuts per face turning axis.
Jet DiamondA "Corner Cube" transformed into an octahedron.
Jumble OctahedronA puzzle with the jumbling only axis system based on the Triakis Tetrahedron.
Leaf OctahedronA hybrid puzzles combining a Curvy Copter Octahedron with a 2x2x2.
Lolo's octahedronA 2x2x2 with an additional layer on each side. It behaves like a subset of a 4x4x4.