Hi!

As you may remember, my Biaxe is a puzzle with a very simple "interface" (2 rotation axes with 4 positions allowed for each) and hard behaviour (due to presence of stored cuts).

Trapentrix is an attempt to make Biaxe at least a little bit easier. It has 2 axes too, but each with only 3 allowed positions. Another difference with Biaxe is that here I decided to truncate the sharp corners to have nice regular pentagonal faces. Actually it does not matter - sharp corners do not bring anything new.

There is an interesting thing about the mechanism. Unlike Biaxe and its close relative Constellation Six, Trapentrix absolutely does not need any fudging when drawn on the Jaap's sphere (when the conical cuts radially go to the sphere's center). But because cutting planes of the solid do not pass through the center, hidden cavities arise between the sphere and the solid's surface. You can see them in the last two pictures.

Why did I call it Trapentrix? Because the faces of this puzzle are TRAPezia, PENTagons and TRIangles. Moreover, playing with this puzzle is a TRAP ENTRY, because it looks deceptively simple, but is really challenging.

I think that this puzzle is my favourite discovery in the irregular geometry. It has relatively few parts, only one cutting plane for each axis and only 4 faces to solve. It neither shape-shifts nor jumbles. There's no bandaging and hidden parts. All you can do is turn one of the two corners left or right. This poor choice makes you feel helpless rather than easy.

Still I could not find any information about this solid and I don't know whether it has a name. Do you?

YouTube VIDEO

Great puzzle with a unique look. Please enable me/us to vote for this puzzle at the International Puzzle Design Competition!

Oskar

What, "easier" with that cut depth?
When looking at the first picture I was about to yell "tridiminished icosahedron", but then I looked at the other pictures and actually read the text. I like the shape, very clever.
I also really like your line of 'simple' puzzles, complexity arising from simplicity. I also like your accent
Summary: I really like it.

Is this another of those "deeper than deep cut" puzzles?

Seems like very difficult......

I would say so. If the shallower part is considered to turn, it would move the other axis of turning.

Other thoughts: this puzzle is a subset of a FTI, explaining the lack of need for fudging. If it were to be "restored" to a full icosahedron, the cut depth wouldn't be that deep.

I love how almost all of your puzzles are tetrahedral based or look related to the tetrahedron. You've found so much complexity in such a simple shape.

Another great puzzle.

On one thread we are discussing the Big Chop and all its complexity, and on this one we have a puzzle with only two faces which can turn, and all its complexity. This forum is brilliant

Very nice puzzle. I really like this one.I'll have to watch the YouTube video when I get home. Do the cavities cause any issues with turning? And if I understand you correctly, you are saying that these cavities could have been filled if you used conical instead of planar cuts, is that correct? If so what would this puzzle look like with conical cuts if this external shape was maintained?

And I agree with Gus. I love how the nature of twisty puzzles hides all this complexity. Its clear (as with the Big Chop) that you can get more complex by adding more. But the ability to find more complexity with less (in this case cut planes) is very counter intuitive. Stuff like this not only gives me a greater appreciation of twisty puzzles and their designers but geometry in general.

On a related note... has anyone done a full scramble and solve on either the Constellation Six or Biaxe yet?

Carl

Beautiful! Brilliant! Amazing!

How has no one thought of this before?! It's such an eloquent and simple, yet perplexing design - the best kind of design.
It is also quite a curious little puzzle - the smaller triangles quite unexpectedly come in two distinct orbits!
It also makes a perfect candidate for my developing theory on relations...

Ingenius build

Peace,
Matt Galla

I was thinking about this
Do you mean comparison with Biaxe? Biaxe has the same cut depth, so yes, this one is easier!
I didn't think this way before, but I see you're right. The solid of Trapentrix can simply be inscribed in an icosahedron and that explains pretty much
No, because each element is connected to the spherical mechanism, where there's not cavities.Correct.It would have all curvy cuts and probably the fixed core part that is normally hidden between trapeziodal faces would be visible. Here's what the conical cuts on the sphere look like:

I can say it for sure about Biaxe - no one, because I possess the only build of this puzzle. I didn't hear about solving Constellation Six, so I admit that someone could have possibly solved it and didn't share There are about 6 copies of this puzzle in total. Wow, really! I couldn't beleive it and checked that, but it is so.

Beautiful. It is amazing how the search for simplicity can find so much complexity!

I also agree that this is deeper than origin turning. It is interesting to note that both this puzzle and the RotoPrism 2 (also deeper cut than origin) share the property of having hidden cavities. I wonder if this is an inherent quality of such puzzles? If any other deeper than origin geometries are found, I will be curious as to whether they will have hidden cavities too.

Playing with this shape in Solidworks, I noticed that it would be possible to slice it differently, creating a shape-shifting puzzle with four axes. I made a couple of "test turn" assemblies, and although it does get blocked often, I believe it could actually be scrambled. I've attached a few images to show what I'm talking about.

Here's the basic shape with one of the axes highlighted:
Here's the shape after one turn on the previously highlighted axis:
And here it is after two turns:
It's hard to see without being able to look around the shape, but there are still available turns.

As a related question, do we have a term for shape-shifting puzzles that do not reveal any inner surfaces after a turn is complete? I think this concept would be such a puzzle, and the TriTangle also qualifies. There must be others too.

David's take on the shape is also icosahedron-based, with these four faces. An interesting shape! Challenge: combine Timur's and David's ones

I found that pytlivyj_1 solved Constellation Six,
see http://twistypuzzles.com/forum/viewtopic.php?f=8&t=20187

It's brilliant.

Thomas

This puzzle is now available in my Shapeways shop (from $83,70 in WSF).

Link

Assembled and stickered version can be ordered directly from me.

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