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.
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