The Face Turning Octahedron (often abbreviated as FTO) is a

combination In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are ...

and

mechanical puzzle A mechanical puzzle is a puzzle presented as a set of mechanically interlinked pieces in which the solution is to manipulate the whole object or parts of it. While puzzles of this type have been in use by humanity as early as the 3rd century BC ...

. Unlike cubic puzzles, the FTO is based on an

octahedral In geometry, an octahedron (: octahedra or octahedrons) is any polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. Many types of i ...

geometry with eight triangular faces that rotate independently. Its deep-cut mechanism and interplay of the various piece types give the puzzle a distinctive solving approach compared to other cubic puzzles. The FTO is notable for being the first octahedral twisty puzzle to feature straight cuts, setting it apart from earlier octahedral designs.

History

The idea for the FTO was initially developed through a series of early patent filings. On February 9, 1982, Clarence W. Hewlett Jr. filed the first patent for a face-turning octahedron, and just two weeks later, on February 24, 1982, Karl Rohrbach filed a similar patent. However, neither patent led to a commercial product which left the concept theoretical for years.

Ernő Rubik Ernő Rubik (; born 13 July 1944) is a Hungarian architect and inventor, widely known for creating the Rubik's Cube (1974), Rubik's Magic, and Rubik's Snake. While Rubik became famous for inventing the Rubik's Cube and his other puzzles, m ...

, the creator of the Rubik's Cube, expressed interest in the development of an FTO. Rubik envisioned a version of the puzzle that incorporated only corners and centers, and a patent was filed on February 9, 1981. On September 15, 1997, Xie Zongliang (謝宗良) from Taiwan applied for a patent for the FTO. According to a report, approximately 1,000 units were produced by Xie in 2008, and there is some indication that the puzzle may have been constructed as early as a decade before that production run. On July 9, 2003, David Pitcher filed a patent for an FTO. However, the patent was never formalized due to non-payment of issuance fees, allowing the invention to enter the public domain. Between 2001 and 2003, Pitcher developed a working mechanism for the puzzle and later claimed that his design was the first functional prototype of an FTO. However, Pitcher's prototype did not enter mass production, leaving uncertainty on whether Pitcher or Xie created the first working prototype.

Mechanism

The FTO consists of three distinct piece types, totaling 42 external elements: * Corner pieces: There are 6 corners, each occupying a vertex of the octahedron * Edge pieces: There are 12 edges that are located on the intersections of the turning planes * Triangle pieces: In addition to the corners and edges, there are 24 triangle pieces that fill the remaining gaps The number of internal components varies depending on the manufacturer.

Number of unique positions

Consider these constraints for calculating the total number of unique positions: Permutations and orientations: * 6 vertices (corners) can be arranged in 6! ways, with 2 orientations each * 12 edges can be arranged in 12! ways * Two sets of 12 centers (triangle pieces) can be arranged in (12!)² ways Restrictions: * Only an even number of vertex pieces can be flipped (division by 2) * Vertex and edge permutations must be even (division by 2) * Centers are grouped in identical triplets (division by 3!⁸) * The puzzle's orientation is fixed by one unique piece, offering 12 possible (division by 12) Combining these factors, the total number of unique positions is:

\frac = 31,408,133,379,194,880,000,000

Records

Although the FTO is not an official

World Cube Association The World Cube Association (WCA) is the worldwide non-profit organization that regulates and holds competitions for mechanical puzzles that are operated by twisting groups of pieces, commonly known as '' twisty puzzles'' (a subcategory of combi ...

event, it has an active speedsolving community, largely due to the resurgence of newer hardware in recent years. As one of the most frequently featured unofficial events at official competitions, there is growing advocacy for the FTO to gain official recognition by the WCA.

Top 5 solvers by single solve

Top 5 solvers by
Olympic average A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, a ...
of 5 solves

{, class="wikitable" !Number !Name !Fastest average !Competition !Times , - , 1. , Aeden Bryant , 14.29s , FMC and More Maine 2025 , (12.57), 13.56, 14.38, (14.93), 15.26 , - , 2. , Michael Larsen , 17.10s , Cubing with Dinosaurs Lehi 2025 , (16.24), 20.71, 16.11, 17.04, (18.03) , - , 3. , Chris Choi , 17.11s , Pittsburgh Winter 2025 , (17.24), 17.45, (22.52), 16.63, 13.77 , - , 4. , Chandler Pike , 17.40s , Orono Open 2025 , (17.07), 15.77, (21.44), 17.17, 17.96 , - , 5. , Dan Pastushkov , 18.12s , {{flagicon, USA Bay Area Side Events Day 2025 , (18.97), 20.76, 17.69, 17.69, (15.72)

References

Mechanical puzzles Puzzles Combination puzzles