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MS>

I am fairly certain that the Pyraminx is a regular tetrahedron. In the

solved state each of the four faces shows only one of the four colours.

ML>

This is correct for all of the *tetrahedral* pyraminxes with only

one small exception: the Star Pyraminx has all middle pieces the

same colour. Meffert used the word "pyraminx" as a prefix to just

about all the puzzles he either conceived or planned to market.

MS>

The Pyraminx Star was described as a Pyraminx without the centers.

So I guess each face of the Pyraminx Star looks as follows.

+ / \ / \ / V \ / \ +---------+ / \ / \ / \ M / \ / E \ / E \ / \ / \ +---------*---------+ / \ / \ / \ / \ M / \ M / \ / V \ / E \ / V \ / \ / \ / \ +---------+---------+---------+

ML>

Actually the above diagram is a good representation of a head-on

view of the popular or standard pyraminx (I've taken the liberty

of embellishing it a little).

There are 4 Vertices (3 colours), 6 Edges (2 colours) and 12 Middle pieces (single colur) so there are 12 + 12 + 12 = 36 facelets.

The tips (or small vertices) can rotate independently, and the larger

turn includes the rotaion of the adjacent 2 edge pieces and single

middle piece. The small tips each have 3 positions, it's adjacent

middle piece also has 3 positions, and the 6 edges obey the same

basic laws as the cube, so there are:

3^4 * 3^4 * (6!/2) * (2^6 /2) = 75,582,720 combinations or approximately 75.5 million (993,120 for the snub version)

The math for the pyraminx octahedron is very similar, though

it has 4 positions for the 6 vertices and middle pieces

and 12 edges:

4^6 * 4^6 * (12!/2) * (2^12/2) = 8,229,184,826,926,694,400 or approximately 8.2 quintillion.

So the snub pyraminx (or if you prefer "The Pyraminx Snub") would

look like:

+---------+ / \ / \ / \ / \ / \ / \ / \ / \ +---------*---------+ \ / \ / \ / \ / \ / \ / \ / \ / +---------+

One could imagine snub octahedrons as well.

MS>

I have no idea what Pyraminx Senior and the Pyraminx Master look like.

ML>

They are visually indistinguishable from the standard pyraminx,

however information on the Senior Pyraminx is exceedingly sketchy.

I've never seen a photograph of a Master Pyraminx in the middle

of an edge turn so I rather doubt a working prototype was ever

made, but you never know...

I'll take a stab at one more calculation...

The pyraminx hexagon has 12 corners and 18 edges and 8 centres. Each side has 13 facelets so there are 13 * 8 = 104 total facelets. 12!/2 * 3^11 * 16! * 2^15 = 29,087,761,395,446,975,811,708,518,400,000 or approximately 29 nonillion (29^30). -> Mark <-