A "Tetrahedron" twisty-puzzle is, overall, a regular tetrahedron (no surprise there) which has the following key properties:
There are several variations of this puzzle, each described in some detail further below. But a quick summary is:- 4 equilateral triangle faces (identical, except for color) -- an equilateral triangle is a regular polygon of 3 sides
- 6 edges (each a line where two faces meet)
- 4 vertices (each a point where three edges meet)
triangular base (and 4 faces). This contrasts with the Great Pyramids of Egypt which each have a square base (and 5 faces).Like all twisty puzzles discussed on my site, each face is divided into multiple facets which are (for this class) colored triangles each identical in shape and size. The goal is to arrange the facets (by twisting layers) such that every face shows a single color. Most tetrahedron puzzles (all discussed here) have four unique colors (one for each face). - Mini-minx / Junior-Pyraminx [n=2] (2
^{2}=4 triangles per face * 4 faces = 16 triangles; 4 tetrahedrons + 1 octahedron = 5 surface blocks) - Pyraminx [n=3] (3
^{2}=9 triangles per face * 4 faces = 36 triangles; 4+6=10 tetrahedrons + 4 octahedrons = 14 surface blocks) - Master Pyraminx [n=4] (4
^{2}=16 triangles per face * 4 faces = 64 triangles; 4+12+4=20 tetrahedrons + 4+6=10 octahedrons = 30 surface blocks) - Professor's Pyraminx [n=5] (5
^{2}=25 triangles per face * 4 faces = 100 triangles; 4+18+12=34 tetrahedrons + 4+12+4=20 octahedrons = 54 surface blocks)
Most important, the Tetrahedron ("Pyraminx") family of twisty puzzles is built of two different types of building blocks:
- Regular Tetrahedron (pyramid with a 3-sided base; 4 triangular facets total)
- Regular Octahedron (two pyramids, each with a 4-sided base, fused together at their bases; 8 triangular facets total)
Note that both of these building blocks are a Platonic solid. Two interesting things about any Platonic solid: all faces have the same shape and each vertex (corner) has the same number of faces. In particular for this puzzle class:
- both Tetrahedrons and Octahedrons have facets which are equilateral triangles
- Tetrahedrons have 3 triangles converging at each vertex and a total of 4 triangular facets (see 1
^{st}image on right) - Octahedrons have 4 triangles converging at each vertex and a total of 8 triangular facets (see 2
^{nd}image on right)
In summary, although each puzzle of the Tetrahedron ("Pyraminx") family appears to be composed of identical blocks ("cubies" in the popular twisty-puzzle lingo), each Tetrahedron puzzle is actually composed of two different types of blocks: tetrahedrons (same shape as the overall puzzle) and octahedrons (very different shape, but each facet is still an equilateral triangle). In other words, every exposed facet of the different blocks is an equilateral triangle, and because they are all the same shape (and size) the whole puzzle The irony, in my opinion, is that the tetrahedron puzzles are conceptually more complex (2 block types) than the cube puzzles (1 block type), Uniquely, the tetrahedron ("Pyraminx") puzzles are the only ones which are fully Dual-Turning. That is, you can rotate Finally note that I said the tetrahedron puzzles are "fully" Dual-Turning (all layers operate the same). It is conceivable that another Platonic Solid (like an octahedron) could be built as a Dual-Turning twisty puzzle. I do not know of any which actually exist, but if one were to be constructed, it would have to built from non-Platonic (irregular) blocks. I think of such a construct as impure (not built from blocks of Platonic Solids). An actual example is the Icosaix (which has an overall icosahedron shape). It allows twisting of both corners and faces, but the corners can not turn in layers (only the "trivial" tips) and thus I consider that puzzle to be mainly Face-Turning (or "very limited" Dual-Turning). All of the tetrahedron twisty puzzles, except for the Mini-Minx, lack fixed center blocks. As far as the number of combinations go, you might expect these puzzles to have values divided by 12 (4*3) to account for no fixed orientation like the way a "center-less" cube puzzle has its combinations divided by 24 (6*4). No "orientation" divisor is needed for any tetrahedron puzzle because the orientation is fixed by the four corners! You might think that turning the face of one of these puzzles would move 3 of the corners (which it does), but mathematically this is equivalent to rotating all the layers "below" a face in the opposite direction. The result is the 3 corners on the face remain fixed, and the fourth corner simply rotates in place.
© 2017, H2Obsession Image of "Professor's Pyraminx" from Mefferts.com (http://www.mefferts.com/products/), provided under copyright fair use. |

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