Part 1 - Align Corners
There are four corners on the pyraminx. The first step towards solving the pyraminx is to make all three stickers on the corner piece align with the adjacent stickers of the adjoining piece. This should take at most 1 move per corner.That means this:
...will become this:
Do this for All four of the corner pieces. After doing this, there is no reason whatsoever to turn the outer corners again for the rest of the solution.
If you're trying to solve a tetraminx, you can ignore everything I just said.
The following segments are called the intermediate corners. These are represented by the shaded in areas of this picture...
Twist the pyraminx/tetraminx so that the intermediate corners line up on each side. This should make something like a Mitsubishi logo on each side like this.
Mitsubishi!
Tip:
Do you find it hard to determine what color a side will end up? (i.e. you line up 2 blue intermediate corners and you try to align the third corner but it doesn't have any blue on it) Look at the corner piece on the opposite side. There are 3 stickers on it. The color of the opposite side will be the color that is missing among those 3 stickers. Look at the picture above for example. The corner in the middle of the picture has blue, red, and yellow on it. The missing color is green. Therefore the opposite side is green.
Part 2 - Solve a Base
Once you've got the little mitsubishi logos in place, you need to pick a base color. In the examples, I'll be using blue.The next 2 steps will focus on positioning the pieces between the intermediate corners from the previous step. In the future, I will call these the 'edge pieces' or 'edges'.
This step will solve the three edges on the bottom. In this picture I have selected blue and I am holding it so that blue is on the bottom.
Now we're going to solve the purple area.
Look for an edge piece in the orange region pictured above that has your base color on it. (In my case, blue) The probability of not being able to find a base colored edge on the top row is 1 out of 20.
After you find it, take note of the color of the other sticker on this edge. Let's say for example you find a blue edge piece that also has a yellow sticker on it. Hold the pyraminx so that the yellow-face-to-be is in front and the blue face is still on the bottom. Now turn the top so that the blue/yellow edge is in front and the blue sticker is facing you. Like in this picture...
...or it could possibly look like this...
If while looking at the yellow face, the blue/yellow edge is on the left, do this...
(Illustrations show front and right faces)
If while looking at the yellow face, the blue/yellow edge is on the right, do this...
(Illustrations show front and right faces)
Continue this until all the base colored pieces on the top row are on the bottom row. If a piece you need is already on the bottom row but in the wrong place or the wrong orientation, put a random piece from the top row in its place with the method above. The piece you need will now be available on the top row.
You should have something that looks like this...
Part 3 - Placing the top edges
There are a couple of possibilities of what your top 3 edge pieces look like now. (Make sure your top corner is turned so that you still see the Mitsubishi logos)Case A:
It's solved.
Case B:
1 edge piece is 100% correct and the other two need to be flipped
Case C:
1 edge pieces is 100% wrong and the other two have 1 sticker that lines up with the adjoining side.
Case D:
All 3 are completely wrong but when you turn the top corner, they will line up with the bottom perfectly.Solution to Case B:
Hold the Pyraminx so that the two wrong pieces are at the bottom and the left like this...
And then do this...
Solution to Case C:
Hold the cube so that the two edges that have one sticker that line up are in the same place as Case B. Then do the moves for Case B. After that it should look like Case D.Solution to Case D:
There are two possiblities here...
In this case do this (colors don't have to match the example)...
And the other possible direction:
In this case do this (colors don't have to match the example)...
And that's all there is to it.