Leaf OctahedronA hybrid puzzles combining a Curvy Copter Octahedron with a 2x2x2.
Lilac OctahedronA face-turning elongated square bipyramid. Twelve axes, eight of them jumbling only.
Lolo's octahedronA 2x2x2 with an additional layer on each side. It behaves like a subset of a 4x4x4.
Master Skewb diamondA master skewb transformed into octahedral shape. Also appropriately described as face turning octahedron with central face pieces.
Mini Master OctahedronAfter the Master Octahedron from the same inventor another 5x5x5 transformed into the shape of an octahedron.
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