Invented independently in 2004 by Mike Grimsley and Shotaro Makisumi, this is a simple yet very fast method to the Pyraminx.
Step 1:
Place 4 corners in one "layer" with their orientation corrected.
a (Grimsley). find adjacent corners with two colors matching, build from there.
b (Makisumi). two opposite corners with no same colors, the other two corners must be opposite to the colors on the sides.
41 1| |4 2| |3 32
Average about 7 moves
Step 2:
Permute the remaining 4 pieces correctly (orientation does not matter).
1/6 Oriented correctly (0)
4/6 Adjacent swap RU'R'U'F'UF (7)
1/6 Diagonal swap FRUR'U'F'U (7)
Average=((0)1+(7)4+(7)1)/6=35/6=5.83bar
+0.75 AUF =>
Average: 6.583bar
Step 3:
2 moves to solve.
Total: 15.583bar moves on average