Pyraminx

There are 933,120 different positions (disregarding the trivial rotation of the tips), a number that is sufficiently small to allow a computer search for optimal solutions.

The table below summarizes the result of such a search, stating the number p of positions that require n twists to solve the Pyraminx:[2] The world record single solve is 0.73 seconds, set by Simon Kellum of the United States at Middleton Meetup Thursday 2023.

The world record average of five solves (excluding fastest and slowest) is 1.27 seconds, set by Sebastian Lee of Australia at Maitland Spring 2024.

The centers of the fourth color are then solved using the slot formed by the non-permuted edge.

The simplest, Tetraminx, is equivalent to the (3x) Pyraminx but without the tips (see photo), resembling a truncated tetrahedron.

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.

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).