Minx Minx & Minx

A Pyraminx Crystal, Megaminx, and Pyraminx

Can you find the goldfinch in the picture?

See the birdbath? See the feeder behind it? See the Rosemary behind it? See the Goldfinch on the Rosemary directly above the feeder?

By the way, these are not the only puzzles I have that are minxes. Maybe I should get them all out together for a big minx scramble and solve sometime. 

Skewb Pyraminx Family

April 9, 2017

So I have 6 or 7 puzzles that are in the Pyraminx/Skewb family. I call it a family because their guts are the same. At least I think they are. Haven't had them all apart or done extensive research online. I have written posts about some or all of these before and even included videos, but that is all old news. In fact, Solution 1 and Solution 2 below are from years ago. My new interest is in light of a new interest in solving the cube using mainly Up Replace Down, and The Move, aka The Edge Piece Series, aka Al Bob Charlie aka Up Replace Down GoBack. So I wanted to see if I could do the same with Skewbs. The answer: pretty much. The puzzles are pictured and numbered above. 

1. The Pyraminx is easiest. Just some simple twists followed by a few ABCs. (ABC = Al Bob Charlie, my current name for the Edge Piece Series, or The Move)

2. Then comes the Meier-Halpern Pyramid (Meffert's version is popular and known as Jing's Pyraminx). It is like a Pyraminx with centers so there are 4 more pieces to deal with at the end but they are one color each so a Triple-ABC does a double swap if necessary and it is done. This assumes you start by solving it like a Pyraminx, ignoring the centers until the end.

3. Next is the Skewb. It is a cube shaped Meier-Halpern Pyramid. It has 8 corners 4 of which are attached to the core like a pyraminx, which can similarly be solved with a few simple turns. The 6 square center pieces can be solved with ABC just like the edges of a Pyraminx. The catch is that you have to twist the solved corners, not the other ones, while solving the squares, otherwise the solved corners will get scrambled. To solve the last 4 corners if they are not already in the right places use a Triple-ABC to double swap them. Then a couple strategic Double-ABCs can be used to twist them if necessary. The exact strategy came by thinking about the Double-ABC. Which way does it twist which corners? How could the cube be manipulated so that two corners only could be twisted while the others were untwisted? Double-ABC leading with the right hand. Roll the cube so the top corner in back rolls to the bottom left and the bottom right rolls to the top back. Then Double-ABC leading with the left hand. Two of the four twisted corners get untwisted by the left-handed move. And the squares that moved about by the right-handed moves get put back by the left.

4. The Skewb Ultimate is a Skewb in the shape of a dodecahedron. That is a 12-sided Skewb. Four of the small corners can be easily solved like the first four corners of the Skewb. Then the big pieces can all be put into place using The Move. It matters not whether they are oriented correctly at this point since when solving the last 4 corners the big pieces can get flipped. So after solving the last 4 corners flip the big pieces.

5. The Squished Skewb has to be solved like the Skewb Ultimate because its odd shaped center pieces can get flipped. It is also tough to solve because of its large size. And it shape-shifts because of its squishedness. But at least the pieces resemble those of a normal Skewb.

6. The Skewb Curvy Rhombohedron is by far the quirkiest of the Skewbs I own. First I want to say that it is not a rhombohedron. Maybe kite-o-hedron would be a better name, but whoever heard of one of those! At any rate there are six faces all of which are kite shaped. There are 3 different shaped pieces. Six triangles in the center of the kites, two small corners, and six large corners. The six large corners correspond to the six squares of the Skewb. The two small corners and six triangles correspond to the eight corners of the Skewb. Oh, did I mention it shape-shifts? Like the Skewb Ultimate the big corners can flip while solving the last 4 pieces. But then there is something else I have encountered that I did not on any of the other skewbs. Instead of a double swap I have had to twist a face at the end to get the last 3 corners solved. Then I have to resolve the "edges" that shift around. Very quirky indeed. Fun. The reason this happens is because the triangle center/corners don't have obvious orientation like the other skewbish puzzles have. If you make sure all 8 "corners" are solved in the beginning then that won't happen at the end.

7. There is one more puzzle with the word Skewb in the name, but it is not very skewbish in my mind. The F-Skewb. It is cut in such a way that it can be scrambled and solved exactly like a Skewb, but there are additional cuts that allow for non-skewbish scrambling. Four little corners can be solved easily like the first four of the Skewb. Each center Skewb square is elongated and cut in half so there are 2 squares per side. I think they can all be solved using The Move. More testing is required. Then the final four corners are each cut into thirds. I can solve them after all else is solved using a commutator I devised when solving the Face Turning Octahedron. The commutator is very much like the one used to 3-cycle corners of a cube.

The following was written years ago when I had a different take on the whole thing. My current favorite solution starts out like Solution 1, but when it comes to the last 4 corners is much simpler than the following. There are not cases and no jumping about. Simply permute then orient the corners. I must admit that with the Curvy Kite Skewb I frequently have to 3-cycle corners at the end instead of doing a double-swap. I twist them into place, use the Move to put the three big pieces back and finish it up. As I think on it, I seem to recall a way to avoid this situation. After solving the first 4 pieces check to see if the last 4 need to double-swap or 3 cycle.

Skewb Solution 1: (This is based on the Crazy Tetrahedron Method I learned from rline.)

Centers: First 4 Corners

Get two opposite corners on one face. This takes at most two twists. Get the two skew corners on the opposite face. This takes at most two twists.

Edges: 6 Center Squares

Use EPS making sure you twist the centers solved in the Centers section, and not the Corners that will be solved last. In the Crazy Tetrahedron and the Jing's Pyraminx, it is easy to tell centers from corners, since centers look like centers and corners look like corners, but that is what makes the Skewb challenging. The centers and corners all look like corners and all are centers of rotation.

Corners: Last 4 Corners

Hold the puzzle with a Center forward on the bottom, and 2 corners on bottom with one on the right and one on the left. Another center is on the upper left, and one on the upper right. Call the one on the left L, and the one on the right R. ( L'RLR' ) x 3 will swap the two corners on the bottom with each other, and the two on the top with each other. The colors on the corners on the front faces on the bottom will move to the bottom after the swap, so it is preferable they are the same as the edge on the bottom. The colors on the top of the front top corner and back top corner will stay on top.

Case 1: All are in the right place but at least two are twisted. Hold two twisted corners on top, and do ( L'RLR' ) x 3. Go to Case 2.

Case 2: Double Swap needed.

Holding the two bottom corners and top front corner still, twist the back half of the puzzle so the edge on top matches the color of the top corner that is in front.

( L'RLR' ) x 3 If necessary, go to Case 1.

Case 3: One is in the correct place, and may or may not be twisted.

Twist the Half which will place all 4 corners in their correct spots. They may or may not be twisted. Use setup moves and EPS to re-solve the edges. Go to Case 2.

Solution 2 (This is the solution I came up with on my own originally.)

Notation: Hold the Skewb so one face is facing you, and so there is a corner pointing right, one pointing left, one pointing up, and one pointing down. We will name these corners Rf, Lf, Uf, and Df, respectively. The corners behind these corners are in the back so we will name them Rb, Lb, Ub, and Db. Twists are defined by the corner that is the center of rotation for the twist. Centers can be named Ru, Rd, Lu, Ld, F, and B.

First 4 Corners

• Get two opposite corners on one face. This takes at most two twists. Get the two skew corners on the opposite face. This takes at most two twists.

Place the Last 4 Corners

• Rb Lb Rb' Lb' swaps Rf with Lf and Db with Ub, and twists Lf, Ub, and Db counterclockwise.

Twist the Last 4 Corners

• ( Rb Lb Rb' Lb' ) x 2 twists Rf and Lf anti, and Db and Ub clockwise.
• ( Rb Ub' Rb' ) Df ( Rb Ub Rb' ) Df' twists Rf anti and Lf clockwise. This is a very easy to see what is happening algorithm. Move Rf up; Twist it; Move it down; Replace it with Lf; Move Lf up; Twist it; Move it down; Move it back.

Place the Centers

• [ ( Rb Ub' Rb' ) Db ( Rb Ub Rb' ) Db' ] x 2 moves Lu > Ld > Rd. I hold my left thumb on F throughout. I go for 3 centers in a row, rather than 3 adjacent centers, but if I end up with 3 adjacent I can use a setup move when placing the last 3.
• ( Rf' Lf Rf Lf' ) x 2 Df ( Lf Rf' Lf' Rf ) x 2 Df' moves F > Ld > Lu. That is, it moves 3 centers around a corner without scrambling anything else.

Pyraminx

On January 18, 2010 I posted this on WordPress. Today as I read through it, it made me smile. I guess you could say it made me laugh at myself.

My strategy has changed. Now I solve all the corners with a few twists, then all the edges in no particular order. I still use the Move for the edges.

The Pyraminx is a colorful, twisty tetrahedron, or pyramid.

The little corner tips can rotate, but are always attached to the same pieces, so when I think of a corner piece it is the tip plus the piece it is attached to. There are three edge pieces surrounding each corner. A corner and its edges make up the small pyramid that, along with the base, makes up the whole puzzle. The base is comprised of all the pieces that have the same color. The base has three corners and three edges, one edge between each pair of corners. So if the base has 6 pieces and the small pyramid has 4, there are 10 pieces to the puzzle altogether. You can also see it as 4 corners and 6 edges. Each piece has a home spot. Every piece is home when the puzzle is solved. We call a piece the owner of its home. When the puzzle is scrambled, at least some of the pieces are visitors. That is, they are not in their own home spots, but in another piece's home spot.

In my cube ramblings I sometimes refer to online solutions that I have learned or at least looked at. I have not looked at Pyraminx solutions online. The best solution depends on what you are after. Want a strategy that requires the fewest moves? Want a strategy that is good for speed solving? Or do you want to simply figure out on your own how to solve the puzzle, and develop your own strategy for doing it consistently? That is where I am in my puzzling adventures now, so that is why I no longer look at how other people suggest solving a puzzle. Rarely ever. I have included the explanation of how to solve the Pyraminx below to document for myself how I do it. If you want to compare my method with yours for some reason, it is there for you to try to figure out. Or if you have tried to solve the Pyraminx and need help, then maybe this will help.

Solve One Layer

To solve the Pyraminx I like to start with one of the bases. First I solve three corners relative to one another. I think this can always be done in at most 3 twists. Then with those corners on the bottom I insert the edges into place. This usually takes 4 twists per edge. I'm going to call the small 4-piece pyramid on top, the top, as in the top layer. The 6-piece base is on the bottom. To get a base edge piece home that is on top, hold the puzzle so the home spot is in front and spin the top so the piece is in the back. There are two base corners in front, one on the left and one on the right. The left corner along with the three edges that surround it make up a small pyramid that I will call simply, the left. Guess what I mean by the right.

Now the edge piece that is in the top and at the back has two sides, left and right. If the sticker that belongs on the bottom of the puzzle is on the left, turn the left so the visitor comes to the top. Turn the top to replace the visitor with the owner. Turn the left to take the owner home. Guess what you do if the sticker was on the right.

Continue this process until the base is solved.

Solve the Top—Flipping Edges

Now twist the top to solve the final corner piece. It may be that the top edges are solved. It may be that they are in their correct positions but two of them need to flip. Or it may be that none of them are in the correct place. If two need to flip hold the puzzle so they are both on the bottom layer (the base), and so that one of them is in front. Let's call this piece, Piece 1, and the other edge that needs to flip, Piece 2. Turn the right so Piece 1 moves to the top. Turn the top so Piece 1 moves to the back. Turn the right the opposite direction as before. Turn the left so Piece 1's home moves to the top. Turn the top so Piece 1 comes to the front left. Turn the left so Piece 1 goes home oriented correctly. When an edge is flipped it is not oriented correctly. When it is oriented correctly, it is not flipped. Now turn the base so Piece 2 comes to the front. Turn the left so Piece 2 moves to the top. Turn the top so Piece 2 moves to the back. Turn the left back into place. Turn the right so Piece 2's home moves to the top. Turn the top so Piece 2 comes to the front right. Turn the right so Piece 2 goes to the bottom. Turn the bottom so the puzzle is solved.

Whoa! The above is a 14-move sequence. I like it because it makes sense to me. It is logical. I can follow the piece around the puzzle and see why it is flipping. I can use a similar technique on cubes to flip edges and twist corners. But there is another way to flip two edges that only takes 8 moves. Really it takes 9 if you count the roll of the whole puzzle in the middle. But still that is a big improvement movewise and there is something I like about it too. It uses The Move.

The Move start Right (The Move R) = R↓ L↓ R↑ L↑

Let R↓ mean turn the right counterclockwise, so that the edge on the front right goes to the front bottom.

Let L↓ mean turn the left clockwise, so that the edge on the front left goes to the front bottom.

Guess what R↑ and L↑ mean. Guess what The Move L would be.

Let Roll R mean Roll to the Right, which means roll the whole puzzle so the front spins clockwise 120˚.

OK. To flip the edges at the front left and front right positions you can do The Move R, Roll L, The Move L.

Solve the Top—Cycle 3 Edges

What do you do, though, if when you solved the top corner, you had 3 unsolved edges in the top?

Move one of the edges to the bottom and then around to the same side as the other two. (This is called a setup move.) Once all three edges are on the front they can be moved into their proper places using The Move! Just make sure when you move the piece to the bottom and around, that you do it in such a way that exactly two of the three pieces need to flip as they cycle. Roll the puzzle so the piece that does not need to flip is in the top layer and needs to move to the other top edge in front. If it is on the right do The Move L. If it is on the left do The Move R. Then do the two twists necessary to solve the cube. (That is, undo the setup move.)