## Saturday, December 15, 2012

### Bauhinia (Rex) Dodecahedron

The Bauhinia (Rex) Dodecahedron is a beautiful and complex twisty puzzle which is a 12-coloured 12-sided solid.

The Basic Plot

1. Solve bottom face.
2. Solve lower half.
3. Solve upper half edges.
4. Solve upper half petals.
5. Solve centers and triangles.
Step 1: Solve Bottom Face

There are two main ways to solve this puzzle. The first is to solve all the edges first, followed by all the petals, followed by all the triangles. This is a valid method but will probably drive you insane. The edges and petals will be ok but the triangles are a nightmare. There are 60 triangles and this could take a number of years to complete.

The method I'll use in this tutorial will be to build the puzzle up layer by layer. The two advantages of this are that you can see the puzzle taking shape (which is great for confidence-building!) and also that it solves over half the triangles intuitively.

Let's go...

To solve the bottom face we begin by placing the five triangles around the white center. (You can start with any colour you like but I'm choosing white.) To do this, move a triangle to a position where it can be turned up, move the center out of harm's way, turn the triangle up into position, then return the center.

Once the center is surrounded by triangles we can place the petals. These are placed in the same way as the triangles. We put a petal on an adjoining face so that it's ready to turn up into position on the white face. Before turning it up, though, we move the already completed parts out of the way.

Finally, we place the edges. To do this, begin with one particular white edge. It doesn't matter which one, but it helps to learn the colour scheme of your puzzle. The standard colour scheme has white-red with white-blue on its right and white-green on its left. Alternatively, you can tell which edges belong next to each other by looking at the lower equator edges.

To place the edge, move it to just below its position, so that when it turns up into place it will be correctly oriented. If this is not the case, turn it around the adjoining face to the other side, so it is correctly oriented. Now move the existing white face triangles and petals out of the way, turn the edge into position and turn back the white pieces.

This video will take you through the whole process.

Step 2: Solve Lower Half

This section is easily the longest section of the solve (although the end triangles can take quite a while as well). To help, I've put links throughout this hour-long video in case you want to navigate to different sections.

Stage 1: Lower equator edges + surrounding petals

The general idea is to find the edge and make sure it's correctly oriented in its position. Then turn it up so that we can put the correct two petals around it. When we then return it to its position, we will have completed the petals as well as the edges.

If an edge needs flipping, move it up to the top face and back down the other side.

Stage 2: Triangle between two petals on a face

There are only five of these to place. We use edge piece series to move a triangle down into position. The key thing here is to note how triangles move around a center.

We can rotate a triangle around the center of a face as follows:

If we turn two adjoining vertices containing the triangle anticlockwise, the triangle will move two spots clockwise about the center.

if we turn two adjoining vertices containing the triangle clockwise, the triangle will move two spots anticlockwise about the center.

The process is quite simple as you'll see when watching the video.

Once the triangle is where we need it, we can move it down into its correct position using edge piece series.

Stage 3: Two lower equator triangles

We place these triangles very similarly to above.

Stage 4: Two petals

The petals are much easier to place than triangles. Move a petal to a position on the top face directly above the top petal on the lower face. Turn up one of the positions to fill. Using an adjoining face, move the completed triangles out of the way, then rotate the upper vertex to position the petal. Finally turn back the triangles and return the petal to its position.

As always, this is difficult to explain but very easy to see on the video.

Stage 5: Middle equator edges

The middle equator edges may be placed very similarly to the petals. We just use a different vertex to turn the already completed pieces out of the way.

Stage 6: Remaining petal group

This last part involves making a center-triangle pair, then making a petal-triangle pair, then bringing these together, and finally placing the whole group into position. The technique is to use the triangle movement properties discussed above to place pieces where we need them.

The video below will take you through the entire process outlined above from start to finish.

Step 2: Solve Upper Half Edges

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

From here, we can place all the remaining edges using edge piece series. We may need to think carefully about how to complete the last few.

Step 2: Solve Upper Half Petals

The remaining petals may also be placed using edge piece series. Near the end, we need to think through exactly where to position pieces in order to be able to turn them into their place.

Step 5: Solve Centers and Triangles

The final part of the solve is two-stage. The first stage is where we place the centers. We use the corner piece series to accomplish this. It's a very quick process.

The second stage is the longest. This involves cycling triangles around without disturbing anything else. To accomplish this, we'll use an edge piece series, followed by a switch out move, then we'll undo the edge piece series, and finally undo the switch out. The whole sequence is only 14 moves and can theoretically be shortened to 12 moves.

The difficult part of the process is almost always the setup moves required to position the triangles before cycling them.

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 a large number of examples of how to complete your puzzle.

And that's it. Your Bauhinia (Rex) Dodecahedron 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.

1. Truly awesome! You seem to be a puzzle solving machine!

2. Great tutorial. It helped a lot. I went a lot of times wrong being brave trying inverted and mirrored series for the triangles. So I am quite experienced now with the pedals end-game :-)

So I am looking for a new challenge. Do you have any suggestions?

1. New challenge? OK. Have you tried Eitan's Star? That is in my opinion the hardest puzzle in existence! It's \$100 though. Let me know...

2. Okay, Eitan Star it will become. The price is high so I'd better ask this for Sinterklaas (5 dec. Dutch tradition)

3. Excuse me …I've get in a problem.I wander that how to solve the step 3 while the last two edges switch their places. I can solve the flips, but this situation looks impossible...could you teach me solve this problem?
my email is dream13jd@yahoo.com.tw
If you could tell me how to do, I will appreciate you very much.

1. Hi there
The situation is impossible. It's happened because you've solved it using the wrong colour scheme when placing your edges on the 1st face. You'll need to re-solve those edges unfortunately. Let me know if this doesn't make sense.

4. Thanks as always. After two days playimg with it, i was able to finish it thanks to your videos. Thanks a million !

5. How do you place the top face center if it isn't correct from the start like yours was?