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 Post subject: Split Hex by OSKAR
PostPosted: Sat Sep 11, 2010 9:24 am 
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Hi Twisty Puzzles fans,

Split Hex is a variation to Hex Cube, which was presented at the Twisty Puzzles Forum earlier. The geometry of Hex Cube and Split Hex forms the basis of Mixup 2x4x4.

Split Hex is a twisty puzzle with forty squares and eight triangles. The puzzle has two hexagonal cross-sections and one four-fold symmetry. It was designed by cutting each of the ten square panels of Hex Cube in four.

Unfortunately, the puzzle is a bit too small for comfort. Some of the turns are hard to make, and take some patience.

Watch the YouTube video.
Buy the puzzle from my Shapeways Shop.
Read more at the Shapeways Forum.
Check out the photos below.

Enjoy!

Oskar
Attachment:
Split Hex - prototype - view 1.jpg
Split Hex - prototype - view 1.jpg [ 48.6 KiB | Viewed 2308 times ]

Attachment:
Split Hex - prototype - view 2.jpg
Split Hex - prototype - view 2.jpg [ 51 KiB | Viewed 2308 times ]

Attachment:
Split Hex - prototype - view 3.jpg
Split Hex - prototype - view 3.jpg [ 50.37 KiB | Viewed 2308 times ]

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Last edited by Oskar on Sat Sep 11, 2010 9:30 am, edited 1 time in total.

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 Post subject: Re: Split Hex by OSKAR
PostPosted: Sat Sep 11, 2010 9:25 am 
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Hooray, I like it more than the first! :D

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PB: At home (In Competition)
2x2 1.xx (2.88)
3x3 11.xx (15.81)
4x4 1:18.26 (1:24.63)
5x5 (3:00.02)
6x6 4:26.05 (6:34.68)
7x7 6:38.74 (9:48.81)
OH (35.63)

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 Post subject: Re: Split Hex by OSKAR
PostPosted: Sat Sep 11, 2010 9:30 am 
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Good work Oskar! Are you ever going to run out of ideas? :lol:

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3x3x3 average of five: 8.92 seconds.
3x3x3 average of twelve: 9.77 seconds.

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 Post subject: Re: Split Hex by OSKAR
PostPosted: Sat Sep 11, 2010 9:52 am 
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Nice... I think my favorite of this family is the Mixup 2x4x4 just due to the shape and color pattern. Could this be shape modded into an elongated octagon such that the 8 color version had each color on a single face (in a single plane)? I'm not 100% sure that's possible but if so I think I'd like that shape more and it would probably make the puzzle just a bit bigger. I'm just not a fan of having the same color on multiple planes.

And for a second there I thought I was onto a new puzzle. Using this line of though...

The Mixup Cube is to the 3x3x3 what the Hex Cube is to the 2x3x3.

Ask yourself what fits here...

The Hex Cube is to the 2x3x3 what the __________ is to the 2x2x3.

The answer is much more boring than I had hoped and it already exists or I'm sure Oskar would have already made one.

Carl

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 Post subject: Re: Split Hex by OSKAR
PostPosted: Sat Sep 11, 2010 5:24 pm 
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AHA!!!!!! So you CAN turn a middle slice of a split hex by 30 degrees and then spin a perpendicular slice. This has never been shown before but I couldn't see why it wouldn't be possible. So a similar thing can occur on a Mixup2x4x4, right?

And Carl, I think the puzzle you are looking for is nothing more than a standard 2x2x3. Long and possibly somewhat boring explanation follows, except for Carl and possibly Andreas or a few others: (and I used pretty simple terms here because I've had a long day... don't judge my lack of clever wordings :lol: )

Let's look at the mixup/hex family that Oskar (and/or Bram?) has discovered/created....

In all cases so far, there is an underlying 2x2x2 mechanism. This extends out to become the corners of each puzzle. All other pieces belong to "rings" of pieces that encircle this 2x2x2 mech perpendicular to the x,y,and/or z axes.

Mixup 3x3x3: 3/3 rings of pieces are present. This means each piece in a given ring has 8 places to line up: 4 that line up with the corners (making what appear to be edges) and 4 that line up with the intersections of the other 2 rings (making what appear to be centers). This gives 8 pieces per ring, and means the rings can move in multiples of 45 degrees (note these 8 pieces are mechanically identical). Furthermore, the inner 2x2x2 has the full symmetries of having all three rings present and thus can always move in 90 degrees

Hex Cube: 2/3 rings of pieces are present. This means each piece in a given ring has 6 places to line up: 4 that line up with the corners and 2 that line up with the intersections of the other 1 ring. This gives 6 pieces per ring, and means the rings can move in multiples of 60 degrees. Furthermore, the inner 2x2x2 only has the symmetries of 2/3 rings (like a 2x3x3) and so can rotate 90 degrees only along one axis, and 180 degrees along the other two.

Split Hex: is a Hex cube with every "ring" cut in half longways (same as taking a 3x3x3 and cutting exactly in half along all 3 axes to get a non-proportional 4x4x4)

Mixup 2x4x4: is a bandaged Split Hex shape-modded up into a rectangle prism. Or if you prefer, a Hex cube that has only been "spilt" in certain places and then shape-modded up into a rectangular prism.

So.....2x2x3 equivalent? Should have 1/3 rings present. This means each piece in this ring doesn't have another ring to line up with, so there are only 4 places (under the 2x2x2 corners) => 4 pieces in the ring that can move in multiples of 90 degrees. The inner 2x2x2 only has the symmetries of 1/3 rings so again can rotate 90 degrees only along one axis, and 180 degrees along the other two. So.... unless I'm mistaken that's just a 2x2x3: the outer 2x2x2 plus a single ring of 4 pieces.
However, it seems to me that you should be able to split the ring of this puzzle just like the Split Hex. Cutting along this ring merely creates a non-proportional 2x2x4, but consider cutting each piece in the ring perpendicular to along the ring (bad description, I know, but I think you know what I mean). Now you have a 2x2x3 where the middle layer can be spun only 45 degrees ;) You can also cut each piece in half both ways => a non-proportional 2x2x4 where each of the middle two layers can be spun 45 degrees. Hmmmm.... you know what? I kinda like that. Both of them. I'm gonna see if I can draw up a mech in CAD once I get my program working again...


Peace,
Matt Galla


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 Post subject: Re: Split Hex by OSKAR
PostPosted: Sat Sep 11, 2010 7:36 pm 
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Location: Marin, CA
Allagem wrote:
Let's look at the mixup/hex family that Oskar (and/or Bram?) has discovered/created....


I can't claim any credit here. The only one of these I had anything to do with was the mixup cube, and that was just giving the general outline of the canonical mechanism.


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 Post subject: Re: Split Hex by OSKAR
PostPosted: Sat Sep 11, 2010 8:54 pm 
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Allagem wrote:
And Carl, I think the puzzle you are looking for is nothing more than a standard 2x2x3. Long and possibly somewhat boring explanation follows... <snip>

We are on the same page. I knew the answer when I posted that and left the answer off hoping to get others to think about it. I got an email asking me for the answer this morning and here is what I had to say then...

Quote:
Think of this chain...

3x3x3
remove one slice layer and you have
2x3x3
remove another slice layer and you have
2x2x3

Now start with the Mixup Cube

Mixup Cube
remove one slice layer and you have
Hex Cube
remove another slice layer and you have
2x2x3

So the answer is 2x2x3. A much more boring answer then I had at first hoped for.

It comes down to the fact that the Mixup Cube has 8 pieces around a slice so you can manage to allow 45 degree rotation.
When you remove the first slice layer you also take 2 pieces out of the others so that leaves you 6 pieces around a slice and you can enable 60 degree rotation.
When you remove the second slice layer you take out another 2 pieces of the last slice layer so it now just has 4 pieces and that limits you to 90 degree rotations which is already present on the 2x2x3 so you haven't made anything new.

So that is what I meant by the answer being boring. I agree if you add the Split Hex into the picture you can make things interesting again.

Without adding Split pieces I wonder if we can take this the other direction. Make a 4D puzzle so you have a Mixup 3x3x3x3. With the 4th slice layer do we now have 10 pieces per slice? Does that allow 36 degree rotation? I have such a hard time picturing 4D puzzles in my head I'm not even sure these questions make sense in 4D. Do you even measure the rotation of a 4D layer of a 4D puzzle in degrees?

Carl

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 Post subject: Re: Split Hex by OSKAR
PostPosted: Sat Sep 11, 2010 9:13 pm 
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what about the mixup version of a 3x3x4?
Let's add another slice layer, or wait, we can't cuz there's only 3 dimensions, huh?

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Last edited by elijah on Sat Sep 11, 2010 9:14 pm, edited 1 time in total.

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 Post subject: Re: Split Hex by OSKAR
PostPosted: Sat Sep 11, 2010 9:14 pm 
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Hmmm... I don't want to side track this thread so if this has been discussed before let me know. I'll start a tread and add the link here in a moment. Look for the Mixup Mater Skewb thread.

Here it is: http://twistypuzzles.com/forum/viewtopic.php?f=9&t=18855

Carl

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 Post subject: Re: Split Hex by OSKAR
PostPosted: Sat Sep 11, 2010 10:06 pm 
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elijah wrote:
what about the mixup version of a 3x3x4?
Let's add another slice layer, or wait, we can't cuz there's only 3 dimensions, huh?

You could add 2 slice layers along the same axis and make a Mixup 3x3x4. The 2 slice layers on the same axis would have 8 pieces each and therefore have 45 degree rotation enabled. The other two slice layers would each have 10 pieces and therefore have 36 degree rotation enabled.

And who says there are only 3 dimentions. I believe a Mixup 3x3x3x3 could be programed and therefore exist as a real puzzle in a computer. And even staying in 3D there are still other ways to add more slice layers... see my post above. They don't have to be all orthogonal.

Carl

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 Post subject: Re: Split Hex by OSKAR
PostPosted: Sun Sep 12, 2010 2:00 pm 
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Great puzzle Oskar! :mrgreen:

I'm adding this to my (imaginary) list of greatest jumbling puzzles ever made.

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