Step 1: Get back to the pyramid shapeEdit
This is almost trivial. Get the corners together in two pairs (there will always be at least one pair), twist them away from each other so as to form a fairly flat shape, then a quarter-twist of the long edge will restore the pyramid shape.
Step 2: Position the cornersEdit
Look for the pair of corners in the correct position relative to each other (those showing the same pair of colours, and such that they either have each pair in one face, or would have if one or both were in the correct orientation). If the other two are not also in the correct position relative to the first two, give that edge a half-turn.
Step 3: Orient the cornersEdit
Hold the Pyraminx in the illustrated position with the corner you want to twist facing toward you (occupying the position which has a purple face in the image). To do a clockwise twist (the purple face at the bottom goes to the left), do (L R' L' R)2; to do an anticlockwise twist (the purple piece goes right), do (R' L R L')2. These sequences should be easy to remember because they start with a turn corresponding to where you want to send the bottom edge, and because of course the second one is the first one backwards.
Step 4: Position the facesEdit
Give the red-yellow edge a quarter-turn to form the flat shape, then give one of the pairs of edges which are together a half-twist, resulting in a shape like a bishop's mitre (or like a short and wide rocket ship). Then look down at the end which has all four faces together; a face is correctly positioned if it is next to the matching corner.
- If all four are wrong, see if twisting the faces will make all four right. Otherwise, return to the flat shape, form the mitre shape using the other pair of edges and try again.
- If only some are wrong, twist the faces until all four are wrong.
Return to the pyramid shape. At this stage, if you haven't solved the puzzle, you have all four faces in the wrong position. Try step 4a again, but this time using the red-green edge, and if that doesn't do it, using the red-blue edge will.