Rubik's Triamid. Introduction

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Grant Reynolds
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http://www.geocities.com/abcmcfarren/math/r90/trmd0.

1 Rubik's Triamid Introduction Scramble the Puzzle Take the Triamid completely apart by breaking it down to its individual components (10 pieces and 4 black connectors). Randomly reassemble the individual components back together into a Triamid again. Rules Pop off a mini-triamid, rotate it in any configuration, and snap it back onto the base. There are 12 different ways to attach the mini-triamid onto the base, and this is what makes tha puzzle so tricky; a side that was once buried can now become completely exposed, and a side that was exposed can now become completely buried. ~Notation~ T+ Rotate the top mini-triamid clockwise (along the vertice). T- Rotate the top mini-triamid counter-clockwise (along the vertice). Page 1 of 3

http://www.geocities.com/abcmcfarren/math/r90/trmd0.htm B+ Rotate the back mini-triamid clockwise (along the vertice). B- Rotate the back mini-triamid counter-clockwise (along the vertice).

R- Rotate the right mini-triamid counter-clockwise (along the vertice).

Notice how the buried side of the minitriamid remains buried afterwards.

2 B+ Rotate the back mini-triamid clockwise (along the vertice). B- Rotate the back mini-triamid counter-clockwise (along the vertice). L+ Rotate the left mini-triamid clockwise (along the vertice). L- Rotate the left mini-triamid counter-clockwise (along the vertice). R+ Rotate the right mini-triamid clockwise (along the vertice). R- Rotate the right mini-triamid counter-clockwise (along the vertice). The first eight moves are somewhat like the Pyraminx puzzle; after popping off a mini-triamid, you must rotate it along the vertice before snapping it back onto the base. Notice how the buried side of the minitriamid remains buried afterwards. The next four moves disobey the laws of the Pyraminx; after popping off a mini-triamid, you must rotate it about the face before snapping it back onto the base. Lf+ Rotate the left mini-triamid clockwise (about the face). Lf- Rotate the left mini-triamid counter-clockwise (about the face). Rf+ Rotate the right mini-triamid clockwise (about the face). Rf- Rotate the right mini-triamid counter-clockwise (about the face). NEXT: Solve the Corners Page 2 of 3

3 Rubik's Triamid Place the Edges A Triamid has 4 corners and 6 edges. Even though each piece is identicle in shape, the corners have three different colors while the edges only have two. By now, all 4 corners are solved and lie at "corner territory" where they belong; forcing the remaining 6 edges at "edge territory", where they belong as well. At this point, the corners are solved, but the edges need to be placed. Step I: Make Each Edge Show Its True Colors Each edge has two sides exposed. Most of the time, some of the edges only show the same color (because the other color is buried inside). They are easy to spot, since they appear to have a "solid" color. Your next task is to reveal both colors of every edge. ~~~~Expose Both Colors of a Single Edge~~~~ Do the Move: Rotate the entire Triamid so that the edge in question is at the bottom-back-left (see diagram). Lf- Rf- Lf- Rf+ Lf- Rf- Lf- Rf+...and the edge is fixed. ~~~~Expose Both Colors of Two Edges~~~~ Do the Move: Page 1 of 4

4 Do the Move: Rotate the entire Triamid so that the edges in question are at the bottom-back-left and the bottom-back-right (see diagram). Lf- Rf- Lf- Rf- Lf- Rf- Lf- Rf- Lf- Rf-...and both edges are fixed. ~~~~Pair Two "Solid Edges" Together (optional)~~~~ Sometimes there are two edges that are hiding their secret identity, but are not always next to each other. You can invert them one at a time, but to save a few moves you can pair them together and fix both of them at the same time. The main reason I've included this step is because the Triamid falls apart way too easy; so my theory is: "The less moves, the better!" Result: Setup: None. Do the move: R- L+ R+ L- Two edge pieces that use to be away from each other are now together. Afterwards, use the same move to Expose Both Colors of Two Edges (as explained earlier). Step II: Place the Edges on One Face To move edges around, use the same exact moves you would noramally do when solving a the Pyraminx. Don't worry, as the same moves are on this very page. Just like the Pyraminx, you must move all the front edges to the front side, but not necessarily at the correct spots. Once all of the front edges are indeed on the front side, then the next phase is to move them into their correct spots, just like the Pyraminx (again)! ~~~~Move All Front Edges to the Front Side~~~~ Move from the back-left: Move from the back-right: Move from the back-top: Page 2 of 4

http://www.geocities.com/abcmcfarren/math/r90/trmd2.

5 B+ L+ B- L- B- R- B+ R+ B+ R- B+ R+ B+ ~~~~Exchange or Swap the Front Edges Around~~~~ Exchange Clockwise: Exchange Counter-Clockwise: Swap Two Edges: R- L+ R+ L- L+ R- L- R+ T- B- T- B+ T+ B- T+ B+ Note: even though the front edges should now be in place, some may still be inverted. This may make the front side appear to be somewhat scrambled, so use the colors of the corner pieces as a guide, to make sure that the front edge pieces are at least in the correct spots. Step III: Place the Rest of the Edges Rotate the entire Triamid so the the old front face is now the new bottom face. Now you can view the other three edges pieces. There are three possilities; two are solvable while the last one is not. Some of the edge pieces may be inverted, so once again use the colors of the corner pieces as a guide. Exchange Exchange Swap Two Edges: Page 3 of 4

6 Clockwise: Counter-Clockwise: Swap Two Edges: B+ T- B- T- B+ T- B- B- T+ B+ T+ B- T+ B+ Parity Error! If you encounter a parity error, then you must go to the page Parity Fix before continuing on. Otherwise... NEXT: Solve the Solve the Place the Parity Solve the Edges Return to Mathematica Page 4 of 4

7 Rubik's Triamid Parity Fix Just like the Square-1 puzzle, you may encounter a parity error near the end. And just like the Square-1 puzzle, I had to refer to Jaap's Puzzle Page to see if there was a quick and easy fix. The answer is: Unlike the Square-1 puzzle, no quick and easy fix exists; as you almost have to start all over again! The Triamid has the Hollywood-style plot-twist ending which is PURE EVIL! In the case of a parity error, you must completely mirror the puzzle. Step I: Swap 2 Corners This is the first step to "mirror" the puzle and define what the new color of each side is suppose to be. Do the Move: Set Up: No set-up is necessary Rf- Lf- T+ Lf- T- Rf+...and two corners are swapped. After the two corners are swapped, use Pyraminx like moves (L+, L-, R+, R-, etc...) so that the corners of one face have matching sides. This will help you figure out what new color each side is suppose to be. Step II: Invert All 4 Corners You know the drill; invert each and every corner by repeating the next move. Page 1 of 3

http://www.geocities.com/abcmcfarren/math/r90/trmd3.htm Rotate the entire puzzle so that the corner is at the lower-left (of the front side). Pop the top to view the buried color of that corner.

8 Rotate the entire puzzle so that the corner is at the lower-left (of the front side). Pop the top to view the buried color of that corner. Snap the top back on, and rotate the entire puzzle so that... The same corner is still at the lower-left, and the color of the bottom side is the same as the hidden color. Do the move... Lf- R+ T+ Lf- T- R-...to invert the corner. Repeat this step for each and every corner. Meanwhile, you will not disturb any of the others corners in any way. Step III: Match the Corners if Necessary Merely use simple Pyraminx-type moves (L+, L-, R+, R-, etc...) to match the sides of all 4 corners. The corners of your Triamid should now be completely mirror-imaged. Meanwhile, the edge pieces are completely scrambled (again!), so you must re-do the entire edge-phase. You could argue that this is bad solution, but you only have to do a parity fix once; and the toll is the same as solving the lowly Pyraminx twice, which is the easiest and quickest of all Rubik-like puzzles. SO ONCE AGAIN... Place the Solve the Place the Parity Solve the Edges Return to Mathematica Page 2 of 3

9 01/01/ :54 PM Rubik's Triamid Solve the Edges The end is near? No, the end is here! All the edges are now in place, and chances are some may need inverting. The best plan of attack is this: Invert pairs of edges first (either adjacent or opposite); that way you only have to use the simple Pyraminx type moves, and solve two edges at the same time to boot. After the smoke clears, there may be a single edge piece left over that still needs inverting, in which case you have to use the more complicated Triamid type move. Step I: Invert 2 Adjacent Edges If two edges that need to be inverted are next to each other, then rotate the entire Triamid so that... Both edges are on the front side. One is at the upper-left, while the other is at the upper-right. Set up: Do the move... Result: R+ T- R- T+ R- L+ R+ L- Both edges pieces are solved! However, be aware that other edges may also be inverted. If so, then either repeat this stage or... Step II: Invert 2 Opposite Edges If two edges that need to be inverted are away from each other, then rotate the entire Triamid so that... Page 1 of 3

http://www.geocities.com/abcmcfarren/math/r90/trmd4.htm 01/01/2007 10:54 PM One edge is on the front side, at the bottom. Another edge is also on the back spine, at the middle. Set up: Do the move.

.. Step III: Invert a Single Edge If only a single edge needs to be inverted, then rotate the entire Triamid so that the edge is on the bottom side, at the back-left (see diagram).

10 01/01/ :54 PM One edge is on the front side, at the bottom. Another edge is also on the back spine, at the middle. Set up: Do the move... Result: R+ T+ R- T+ L- T- L+ T- Both edges pieces are solved! However, be aware that a single edge might be inverted. If so, then... Step III: Invert a Single Edge If only a single edge needs to be inverted, then rotate the entire Triamid so that the edge is on the bottom side, at the back-left (see diagram). Set up: Do the move... Comments: Lf- Rf- Lf- Rf+ Lf- Rf- Lf- Rf+ You may have to do this move twice before the last edge piece is solved. After the move, the last edge piece is either solved or "solid" (both sides showing the same color). If it is solid, then do the move again, and the edge (and the entire puzzle) will be solved... guaranteed! THE Solve the Place the Parity Solve the Edges Page 2 of 3

Rubik's Missing Link

http://www.geocities.com/abcmcfarren/math/rdml/rubmlk0.htm Rubik's Missing Link Notation For this solution, you must hold the puzzle horizontally, which is a lot cooler than using the term vertically.