Extremely Puzzling - Goetz Schwandtner's Puzzles

Puzzle Group: Twisty Octahedra

This group page provides an overview of probably the smallest group of puzzles that directly resemble one of the platonic solids. The puzzles shown below are all twisty puzzles with the shape of an octahedron I have in my collection. There are some others, but in general this is a very small group. No truncated/extended variants in non-octahedral shape are covered here.
Historic notes:
In earlier times, there have been very few Octahedra: The original "Magic Octahedron" is a tip turning octahedron produced by several companies in the 1980s and it has 5 layers. Also in exisitence for quite a while are octahedra based on a Rubik's 2x2x2 mechanism. Older versions of this include the "Okki Gem" which I don't have, but which is equivalent to the PyraDiamond shown below. The Diamond Skewb has also been around for some time, went out of sale, and eventually came back to sale again. Before it came back into sales, the Moshi Diamond appeared with the same design. There are some custom builds that have been around for some time, like Trajber's Octahedron, the Octaminx, and the Greenhill's Octahedron, and the Rainbow-Octahedron (also called Dino-Octa). Of these, only the Greenhill's octahedron and Traijber's Octahedron have been mass-produced, the other's are still extremely rare custom builds. Some years ago a new face turning variant was inventend in Taiwan and came onto the market. There were many discussions about this puzzle and it is know known as "the" Face-Turning Octahedron, or just "FTO". Another design to appear is an adaption of the Traijber's Octahedron idea to a 4x4x4 cube, and this octahedron is also mass produced. Meanwhile, some new designs have been relased, all of them being based on cubic designs.

In the table below these octahedra are shown, with a reference to the base puzzle on the right (if applicable).

Magic Octahedron
Magic Octahedron DaYan Octahedron
Based on 2x2x2
PyraDiamond 2x2x2
Based on 3x3x3
Traijber's Octahedron Traijber's Octahedron Greenhill's Octahedron Gear Corner Turning Octahedron 3x3x3
Based on 4x4x4
4x4x4 Octahedron 4x4x4
Based on Skewb
Diamond Skewb Moshi Diamond Skewb
Based on Pyraminx
Octaminx Pyraminx
Based on Rainbow Cube
Rainbow-Octahedron Rainbow Cube
Face Turning Octahedron
Face-Turning Octahedron Crazy Octahedron Plus - Mercury
Variation of the Pyraminx Duo/No Edges 3x3x3 Cube
Pyraminx Diamond Pyraminx Duo
Based on 3x3x3 Circle Cube
Octic I Octic III Crazy 3x3x3 Jupiter
Mechanism based on Face Turning Octahedron, name relates to Axis Cube
Mini Axis Octahedron 3x3x3 Axis Cube
Mechanism based on Face Turning Octahedron, name relates to Ghost Cube
Mini Ghost Octahedron Ghost Cube