Because just like there are different types of Cube puzzles (2x2, 3x3, skewb) there are also different Octahederon puzzles (skewb diamond, fto, trajber's octahedron) It would not make sense for a 3x3 to be the dual of all octahedron puzzles.
A dual is basically where the corners of a polyhedron turn into its faces and vice versa. Eg, a cube has 6 faces and 8 corners, and an octahedron has 8 faces and 6 corners. For a puzzle to be the dual of another, its faces need to correspond with the vertex or corners of the other. The dual of a 3x3, which is a face turning cube, would have to be a corner turning octahedron. Specifically, it would be a Trajber's Octahedron.
and you can play around with one here. Edit: click on the TW button to go to the website to turn it.
Its solving method is almost identical to a 3x3, with some caveats. 3x3 and trajbers have the same number of pieces if you count them, but a 3x3 and FTO have different number of pieces, so they cannot be duals.
For FTO's case, its dual is a Rex Cube or Super Ivy cube.
Rex cube and FTO have the same number of pieces. FTO is a face turning octahedron which means that its dual should be a corner turning cube, which rex cube is. Like 3x3 and Trajber, Rex cube and FTO have similar solving methods.
Because just like there are different types of Cube puzzles (2x2, 3x3, skewb) there are also different Octahederon puzzles (skewb diamond, fto, trajber's octahedron) It would not make sense for a 3x3 to be the dual of all octahedron puzzles.
A dual is basically where the corners of a polyhedron turn into its faces and vice versa. Eg, a cube has 6 faces and 8 corners, and an octahedron has 8 faces and 6 corners. For a puzzle to be the dual of another, its faces need to correspond with the vertex or corners of the other. The dual of a 3x3, which is a face turning cube, would have to be a corner turning octahedron. Specifically, it would be a Trajber's Octahedron.
and you can play around with one here. Edit: click on the TW button to go to the website to turn it. Its solving method is almost identical to a 3x3, with some caveats. 3x3 and trajbers have the same number of pieces if you count them, but a 3x3 and FTO have different number of pieces, so they cannot be duals.
For FTO's case, its dual is a Rex Cube or Super Ivy cube.
Rex cube and FTO have the same number of pieces. FTO is a face turning octahedron which means that its dual should be a corner turning cube, which rex cube is. Like 3x3 and Trajber, Rex cube and FTO have similar solving methods.
Also I find the naming convention of 2x2 FTO strange,
Why name it as skewb diamond?
Is it because of the solving method being similar to a skewb and the diamond of the skewb being missing on an octahedron?
