## Thursday, July 4, 2013

### Eitan's Star

Eitan's Star is a beautiful and complex twisty puzzle which is a 20-coloured 20-faced solid. It is the first mass-produced icosahedron. To buy this puzzle, click here.

The Basic Plot

1. Solve lower half.
2. Solve upper half triangles.
3. Solve upper half corners.
4. Solve upper half edges.
5. Solve centers.
Step 1: Solve Lower Half

This section is a fairly long section of the solve.

Stage 1: Bottom corner + Surrounding Edges and Triangles

First we place 5 edges around the chosen corners. These turn up with simple turns. After the 1st edge, we simply push the corner back before turning up the others, so as not to disturb our work.

Once the edges are placed, we place the wide triangles between them. These can be turned up from below, or turned into position when on the same face. We turn the corner+edges to the back of the puzzle before placing the triangles. It's super-simple.

Stage 2: Center + 2 Triangles Below Lower Equator

The general idea is to find the center and put it in its position. Then turn it up so that we can put the correct two triangles around it. When we then return it to its position, we will have completed the triangles as well as the center.

Stage 3: Lower Equator Edges

We use edge piece series to move an edge down into position. Place the edge directly above the corners which is above its position. Then use an edge piece series to place it.

Stage 4: 2 Triangles above Lower Equator Edges

These are especially easy to place. Place the desired triangle so it can turn down into its position, but so that it remains fixed when its position is turned up. Turn up the position, rotate the face, and return it. (Honestly, this is hard to describe, but ridiculously easy to do.)

Stage 5: Corner + 3 Edges + Triangles

This last part involves making a edge-corner-edge triplet, then making a triangle-edge pair, then bringing these together, and finally placing the whole group into position. The technique is to join pieces together bit by bit. It's a fairly difficult process, and probably the most time-consuming part of the lower half.

Stage 6: Final Center+ Triangle

This last part involves making a center-triangle pair, then turning it into its position using edge piece series.

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The video below will take you through the entire process outlined above from start to finish, and convince you that it's logical, doable, and fun.

Step 2: Solve Upper Half Triangles

At this point, the entire lower half of the puzzle is complete.

From here, we can place all the remaining triangles using edge piece series. We may need to think carefully about how to complete the last few, and setup moves are often involved.

I have found there is a nice order to these, and will demonstrate this order in the video below.

Step 3: Solve Upper Half Corners

We use the corner piece series to accomplish this. Hold the puzzle so the "Up" face is a downward pointing triangle. Then perform

U UR U' UL  U UR' U' UL

The most annoying thing about the corners is the setup moves required to orient them correctly.

Note that cycling corners will sometimes displace one or two edges from the lower half.

Step 4: Solve Upper Half Edges

The next part of the solve is by far the longest and most annoying. The edges must (almost always) be placed one by one. There are 30 of them, but had we not placed the lower half edges there would have been 60...

We use the following algorithm to accomplish this. Hold the puzzle so the "Front" face is an upward pointing triangle. Then perform

[FDL'  FL' FR FL FR'    FDL  FL' FR FL FR' ] x 2

The difficult part of the process is almost always the setup moves required to position the edges before cycling them. The sequence itself is very simple and easy to keep track of.

Rather than attempting to explain the description of the piece locations involved etc, I'll leave that to the video. After watching it, you'll have enough examples to show how to complete your edges.

Note that cycling edges will displace some centers from the lower half. You may therefore wish to not bother with centers during the lower half solve, but I've found it's required simply for feeling good about the solve!

Step 5: Solve Centers

The final part of the solve is pure relief. The centers are done last because cycling the edges also displaces centers.

We use the corner piece series to accomplish this. Hold the puzzle so the "Front" face is an upward pointing triangle. Then perform

F FDR F' FDL'   F FDR' F' FDL.

It's super simple and almost impossible for things to go wrong. Even the setups are straightforward.

And that's it. Your Eitan's Star is now solved. I trust this site has been helpful. If you have any questions or want some clarifications, please use the comments to do so.  To buy this puzzle, click here.

1. Your tutorial are great. Unfortunately, I haven't had chance to try it 'cause my nephew scramble my Eitan into a jumbling state where i can't get back to icosahedron shape. Could you make a video on get-out of jumbling.
Thanks

1. Hi Chinh,
I'll consider it! I've pretty flat out at present but I'll give it some thought. Have you considered selling your nephew to buy a new Eitan's Star? Can I ask: have you tried to unjumble it lots, or just a little?

2. I tried to un-jumble the puzzle for few days. I was kept being stuck in the same situation where two block of corner+2 edges+center + triangle (this i don't remember exactly) flipped.
Finally, I decided to tear the puzzle apart and re-assemble it again. Scramble it and use your method to solve it. I finally did it and I need to thank you a lot for the tutorial.

One question, When i solving the puzzle, the corners (the tips) was very easy to self-rotated (because they are loosely attached to the core). How could you fix the corner to the core because I see on your video, the corners are very much secured to the core.

1. Awesome! I'm glad you got it in the end. If you accidentally jumble it again, let me know and I'll go ahead and try and make an unjumbling video...

The tips are definitely movable on mine. It's just part of that puzzle. They're easy to turn and you have to just be aware of it. I mean, at the end of the solve, if you have one twisted corner, then you know you've accidentally twisted one, and can just twist it back into position. So do you think you'll solve Eitan's star again, or is that that?!

2. Of course, I will solve the puzzle again and again until I find it is comfortable and fun solving this puzzle. As the matter of fact, on my second solve I find it a lot easier. However, I will be careful enough so that the puzzle won't be jumble again. I might try to consider to work with jumble when I completely "Feel" this puzzle. For now, I am happy with solving this puzzle non-jumbly.

3. Dear Rline and Chinh,
do you have any simple fix to this problem with corner/tips?
I just started playing with the Star, and I don't seem to be able to make few turns without accidentally rotating them. I don't really understand why they didn't create a support in any shape other than perfectly cylindrical. :-( I'm even considering applying a drop of glue...
Thanks!

4. Paul, the only "fix" I know of is to superglue them on. I think other people have done that.

3. Hi there,

I got my Eithan Star on december fifth and stickered it a week ago.
Things went well on the lower half. It was slightly different to your solution. I just added 1 bottom edge to the 5 corners and inserted them, than I joined 1 triangle and 1 edge and inserted them as pairs. Your solution by joining the five pieces on the top half looked very similar to your solution on the Bauhinia.

Than the triangles. Things went well uptill the last five, but doing the next step I screwed up a corner on the bottom half. Since I now only had to do 4 triangles I decided to continue, because getting the bottom half right would certainly destroy my triangle work on the top. Ending up with 2 triangles to swap. I looked to it for hours and decided that it was too risky, so I reduced the complexity of the endgame of the triangles by inserting an extra step. That worked out. This seems almost identical to the solution of the petals of the Bauhinia. The only difference is that there are 3 triangles, which makes the last triangles on the E. Star much more complicated.

The corners were not that hard. I just ended up 2 corners wrongly orientated. I did not want to cheat by turning them seperately, so I brought one extra corner in the corner end-game and tried again. Now I was left with one corner twisted, so I had to twist it into the correct position.

Done that and now the edges. I had to do 35, because I screwed up a corner on the bottom half earlier. I must say that I escaped a couple of times because I was distracted and because my E. Star does not turn nicely. I got stuck doing the alg. and had to recall many times where exactly I was when I got it turned. Luckely I did not go wrong anywhere.

Than the endgame of the centers. Peace of cake.

Of coarse I also used a pencil and paper to write long setup moves for the edges. However what I avoided was naming the layers like “top”, “half back bottom” etc. That confused me too much. Instead I wrote down the colors (abbreviations) of the 3 triangles on the face that I was turning and of coarse the direction of the clock (cl or a.cl). In this way I was completely free to turn the Star during setup moves and undoing the moves. I also did this for the triangles. I just had be aware that I was cycling triangles, so that another color could appear on a face involved in a setup move. As long as you keep track of which triangles you cycle it also works. When you do the edges you won’t have this problem at all. Of coarse everybody must do it the way he or she feels most comfortable with, but if you also have difficulty with naming the layers I certainly would suggest that you try this.

The alg. to cycle 3 edges is to difficult to understand. Cycling 3 pixels on a Bauhidian is understandable especially if you do it on completed cube. Did you figure the alg. to cycle 3 edges on the Star out yourself?

Thanks for the help of this tutorial.

Best regards, Bart Huitema

1. Hi Bart,
Congratulations! For the edges, I'm fairly sure that I adapted a sequence which Burgo (TP forums) had posted for the bauhinia, after I had posted my solution. His sequence was so nice. I realised it should probably be able to work on this as well. I don't understand why it cycles them, but it's very straightforward to carry out.