An "Octahedron" twisty-puzzle is, overall, a regular octahedron (no surprise here!) which has the following key properties:
- 8 faces (each an identical equilateral triangle, except for color) -- an equilateral triangle is a regular polygon of 3 sides
- 12 edges (each a line where two faces meet)
- 6 vertices (each a point where four edges meet)
I know of 3 variants of this puzzle, each described in some detail further below. But a quick summary is: - Skewb Diamond [n=2] (2
^{2}=4 triangles per face * 8 faces = 32 triangle facets; 6 octahedrons + 8 tetrahedrons = 14 surface blocks) - Face-Turning (F.T.) Octahedron [n=3] (3
^{2}=9 triangles per face * 8 faces = 72 triangle facets; 6+3*2+6=18 octahedrons + 3*8=24 tetrahedrons = 42 surface blocks) - Corner-Turning (C.T.) Octahedron [n=3] (32=9 triangles per face * 8 faces = 72 triangle facets; 6 pentahedrons + 6 decahedrons + 18 tetrahedrons = 30 surface blocks)
I would love to give you a true and full description of the octahedron shape, but words fail me. You really need to hold one in your hand (and examine from multiple angles) to appreciate this Platonic Solid. But I will - the octahedron is the mathematical "dual" of the cube (octahedron has 6 vertices and 8 faces, while cube has 6 faces and 8 vertices)
- "true" octahedron puzzles are built of the same two block types (octahedron and tetrahedron) as the "Pyraminx" puzzles
So though it may "look" like the corners should rotate, they do not, Some non-obvious facts about the "true" (F.T.) octahedron puzzles: - The corner blocks have only 2 orientations each (as opposed to 4 orientations in "false" [C.T.] puzzles)
- The edge blocks have only 1 orientation each (as opposed to 2 orientations in "false" puzzles)
- Each middle/wing block of the same color can only show up on 4 of the 8 faces (as opposed to 7 faces in "false" puzzles)
Hopefully the last fact makes it clear that the colored facets can not fully intermix. Interestingly, the first two facts above also limit the way colors can mix in the same way! So it might not be obvious, but any block type (corner, edge, or middle/wing) will have each color on its visible facet(s) limited to appearing on only 4 of the 8 faces of the puzzle. I call this the "no mixing rule": all the colored facets that belong to the same face (when the puzzle is solved) can only ever appear on that face (the "home" face) or the three triangular faces which touch the "home" face at a vertex. In other words, the colors of a face may never appear on the face opposite of "home", nor on any of the three triangular faces which share an edge with the "home" face. Because of the "no mixing rule" of colors, some variants of the Face-Turning Octahedron have only four colors instead of eight. In these, each color is used on two different faces, but the duplicate colors appear on faces which do not mix colors. I've never played one, but it sounds like a nasty beast that would often confound the player with "parity" errors (you would have to pay very close attention to which of two sets a piece belongs because you couldn't rely on color). There is also a "false" (Corner-Turning) variety of Octahedron twisty-puzzles. I call them "false" octahedron puzzles because The "false" (C.T.) octahedron puzzles do Although the number of combinations is limited by the "no mixing rule" in a "true" (face-turning) octahedron puzzle, many (most?) players find the "true" octahedron puzzle to be It probably sounds illogical to think that a puzzle with notably reduced color combinations (the "true" octahedron) has more combinations than a puzzle which allows almost complete color mixing (the "false" octahedron). The real reason is the "true" octahedron has its 24 middle/wing facets on 24 different blocks (tetrahedron in shape) which can move about with almost complete freedom (only restricted by the "no mixing rule"), while the "false" octahedron has its 24 middle/wing facets on only 6 different blocks (decahedron in shape) which can not change position at all (these "axial" blocks can only rotate in-place).
© 2017, H2Obsession Image of "Diamond Skewb" derived from an image at www.thecubicle.us provided under copyright fair use. |

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