Friday, June 2, 2017

Meier-Halpern Pyramid (Jing's Pyraminx)

Originally posted on September 6, 2011 on my Google site.

Solution 1

This is the original method I came up with. I have some new ideas, so made a new solution (2). Then I decided I liked Rupert's method best for doing the Crazy Tetrahedron and adapted it for the JP (3).

Corners and Centers

Like the Skewb’s first 4 corners, solving the corners of the Jing’s Pyraminx is simple and only requires a few twists. If the centers are not solved after solving the corners, then a double swap is needed. Hold the puzzle so that an edge is in front, a corner is at the top, another at the bottom, another at the back on the right, and the other at the back on the left. We can call the corners U, D, R, and L. Let's call the centers R, L, D, and B. To swap centers R with L, and D with B, do corners R' L R L'. Or you could accomplish the same thing with L R' L' R. Or R L' R' L. Or L' R L R'. Different things happen to the edges with each, so if you want to think about the edges while swapping centers...

Cycling 3 Edges

Hold the puzzle so a center is facing you. That makes 3 corners visible. U, D, and L (starting at top and going clockwise). Or you could think of it as U, R, and D (starting at top and going clockwise). There are 3 edges on front. Call them 1, 2, and 3. Move 1 to 2. Move 3 to where 1 is now. Undo the first move. Undo the second move. Repeat these 4 moves. Example: ( D' L D L' ) x 2 moves 1 > 3 > 2, and leaves the color on the front of 1 on the front. The other two are flipped. This is similar to the EPS move of the Ultimate Solution. It has to be done twice to restore the corners that get swapped each time.

Flipping 2 Edges

If two edges need to flip hold the puzzle so one is between corners D and R, and the other is between corners D and L. Use a setup move if necessary.
R moves the RD edge up. U' moves it away. R' moves its spot back down. D' moves its spot back up flipped. U' moves the RD edge back into its spot. D moves RD and its spot back home, flipped correctly.
U sets up the temporarily scrambled pieces to get unscrambled.
L' moves the LD edge up. U moves it away. L moves its spot back down. D moves its spot back up flipped.

Solution 2

Corners

Like the Skewb’s first 4 corners, solving the corners of the Jing’s Pyraminx is simple and only requires a few twists.

Notation

Hold the puzzle so a center is facing you and three corners are on the bottom. Let's call the one on the bottom right front R, the one on the bottom left front L, and the one on the bottom in the back B. Call the one on top U.

Edges

Hold the puzzle so a center is facing you. That makes 3 corners visible—U, R, and L. There are 3 edges on front. Call them 1, 2, and 3. Move 1 to 2. Move 3 to where 1 is now. Undo the first move. Undo the second move. Example: If 1 is between R and U, 2 is between R and L, and 3 is between L and U, then ( R' L R L' ) moves 1 > 2 > 3, and leaves the color on the front of 3 on the front. The other two roll into place, as it were. This is similar to the EPS move of the Ultimate Solution for solving a Rubik's Cube.
If you are on the last 3 edges and the centers are placed correctly, do 3 > 2, 1 > 3, undo, undo. Do it again. The net result is to cycle 1 > 2 > 3, with 3's front color staying on front.

Flipping 2 Edges

If two edges need to flip hold the puzzle so one is between corners L and R, and the other is between corners B and L. Use a setup move if necessary.
( R U' R' L' U' L ) (twist the base to the right) ( L' U L R U R' ) (twist the base to the left)

Swap Centers

The centers get swapped with every edge 3-cycle, so maybe they are solved, and maybe not. If not, ( R' L R L' ) x 3 swaps the front and bottom centers, and swaps the right and left centers.

Rotating Centers

Hold it so one face is in front, and one is on bottom. The front center will rotate anticlockwise, and the left center will rotate clockwise. Do the following twice in a row. 1. R' L R L' 2. Roll the front to the bottom and the left to the front.
3. R' L' R L 4. Roll the bottom to the right. 5. L R' L' R 6. Roll the front to the bottom and the right to the front. 7. L R L' R' 8. Roll the bottom to the left.

Solution 3 (rline inspired)

Terminology

When you turn a Face of the JP you are turning half the puzzle pieces—3 corners, 3 edges, and a center. The other half is a Corner made up of a corner, 3 edges, and 3 centers.

Centers

Like a Rubik's Cube, the centers always stay solved relative to one another.

Edges

Solve the edges of one color. No algorithms are necessary. Not even EPS. Use EPS with Faces to solve the last 3 edges. Holding a Face on top works well.

Corners

Hold the puzzle with a Face forward and 2 corners on bottom. Call the Face on the left L, and the Face 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 Face on the bottom will stay the same after the swap, so it is preferable they are the same as the center on the front. The color on the front of the top corner will move to the back Face and the one on back to the front.
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 Front Face still, twist the back half of the puzzle so the center on back matches the color of the top corner that is in front.
( L'RLR' ) x 3 If necessary, and if possible, twist the Front Face, or back half, to complete the solve. If necessary, go to Case 1.
Case 3: One is in the correct place, and may or may not be twisted.
Twist the Face 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.

No comments:

Post a Comment