Editing Pyraminx (section)

==Variations==
[[File:Tetraminx.jpg|thumb|A solved Tetraminx.]]
There are several variations of the puzzle. The simplest, '''Tetraminx''', is equivalent to the (3x) Pyraminx but without the tips (see photo), resembling a [[truncated tetrahedron]].  There also exist "higher-order" versions, such as the 4x Master Pyraminx (see photos) and the 5x Professor's Pyraminx.

[[File:MasterPyraminx-Scrambled.jpg|thumb|A basic pattern on a Master Pyraminx]]
[[File:MasterPyraminx-Solved.jpg|thumb|A solved Master Pyraminx]]
The '''Master Pyraminx''' has 4 layers and 16 triangles-per-face (compared to 3 layers and 9 triangles-per-face of the original), and is based on the [[Skewb Diamond]] mechanism.  This version has about 2.6817 × 10<sup>15</sup> combinations.<ref>{{cite web|title=Full List of Puzzles|url=http://www.gandreas.com/iphone/twisty/page2/page2.html|website=gandreas software|access-date=2016-12-31|archive-url=https://web.archive.org/web/20160428094549/http://www.gandreas.com/iphone/twisty/page2/page2.html|archive-date=28 April 2016|url-status=dead|df=dmy-all}}</ref><ref>{{cite web|title=Notes on Twisty Puzzles|url=http://michael-gottlieb.blogspot.com/2008/05/number-of-positions-of-generalized.html|publisher=Michael Gottlieb|access-date=2016-12-31}}</ref>  The Master Pyraminx has
* 4 "tips" (same as the original Pyraminx)
* 4 "middle axials"  (same as the original Pyraminx)
* 4 "centers" (similar to Rubik's Cube, none in the original Pyraminx)
* 6 "inner edges" (similar to Rubik's Cube, none in the original Pyraminx)
* 12 "outer edges" (2-times more than the 6 of the original Pyraminx)
In summary, the Master Pyraminx has 30 "manipulable" pieces.  However, like the original, 8 of the pieces (the tips and middle axials) are fixed in position (relative to each other) and can only be rotated in place.  Also, the 4 centers are fixed in position and can only rotate (like the Rubik's Cube).  So there are only 18 (30-8-4) "truly movable" pieces; since this is 10% ''fewer'' than the 20 "truly movable" pieces of the Rubik's Cube, it should be no surprise that the Master Pyraminx has about 10,000-times ''fewer'' combinations than a Rubik's Cube (43 quintilion in the short scale or 43 trilion in the long scale). The Master Pyraminx can be solved in numerous ways: one is layer by layer like the original one or reducing it to a Jing pyraminx.<sup></sup><ref>Martin Schönert ''[http://www.gap-system.org/Doc/Examples/rubik.html "Analyzing Rubik's Cube with GAP"]'': the [[permutation group]] of Rubik's Cube is examined with [[GAP computer algebra system]]</ref>