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 Post subject: Edge of Insanity (formerly Shallow Madness)
PostPosted: Mon Jun 10, 2013 4:54 pm 
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Hi Everyone,

My latest puzzle is based on the "Madness" series of puzzles by Oskar. First was More Madness, which is a face-turning trigonal dipyramid. Next Oskar made Deeper Madness, based on the same geometry, but with the slice planes moved slightly past the origin of the puzzle. The result was a puzzle that is difficult to classify. Is the geometry deeper-than-origin-cut, or is it shallow-cut? I then made Edge of Insanity by moving the slice planes even further past the origin. As the puzzle name implies, this puzzle is clearly edge-turning and shallow-cut. Even though the slice planes are aligned with the faces, the centers of rotation are the six edge pieces. These pieces are attached to the core, just as the face centers of a standard cube are attached to the core. To use Edge of Insanity as a face-turning puzzle, you would have to hold one axis still and turn the other five axes and the origin. This is why I say it is clearly a shallow-cut puzzle.

Here is a video of the puzzle.

You can buy Edge of Insanity in my Shapeways shop.

Despite the smaller number of pieces in the puzzle, it is still complex to solve, and not even too easy to unjumble. The nice thing about the puzzle is that there are no hidden parts to block any axes. But there is occasional overhang bandaging to worry about. Of course, Edge of Insanity transforms into many unusual shapes while being played. Here are a few pictures:
Attachment:
Shallow Madness cool side.JPG
Shallow Madness cool side.JPG [ 191.15 KiB | Viewed 1491 times ]
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Shallow Madness hot side.JPG
Shallow Madness hot side.JPG [ 201.21 KiB | Viewed 1491 times ]
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Shallow Madness mid-turn.JPG
Shallow Madness mid-turn.JPG [ 201.21 KiB | Viewed 1491 times ]
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Shallow Madness one turn.JPG
Shallow Madness one turn.JPG [ 197.68 KiB | Viewed 1491 times ]
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Shallow Madness two turns.JPG
Shallow Madness two turns.JPG [ 184.36 KiB | Viewed 1491 times ]
Attachment:
Shallow Madness scrambled.JPG
Shallow Madness scrambled.JPG [ 200.75 KiB | Viewed 1491 times ]
Attachment:
Shallow Madness jumbled 1.JPG
Shallow Madness jumbled 1.JPG [ 185.19 KiB | Viewed 1491 times ]
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Shallow Madness jumbled 3.JPG
Shallow Madness jumbled 3.JPG [ 181.91 KiB | Viewed 1491 times ]
Attachment:
Shallow Madness jumbled 4.JPG
Shallow Madness jumbled 4.JPG [ 209.68 KiB | Viewed 1491 times ]
Attachment:
Shallow Madness scrambled side view.JPG
Shallow Madness scrambled side view.JPG [ 193.67 KiB | Viewed 1491 times ]
Attachment:
Shallow Madness scrambled 3.JPG
Shallow Madness scrambled 3.JPG [ 199.93 KiB | Viewed 1491 times ]

Enjoy!
Dave

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Visit Pitcher Puzzles where you can buy the IPP award-winning RotoPrism 2, Fracture-10, and many, many more.


Last edited by David Pitcher on Thu Jun 20, 2013 12:27 pm, edited 1 time in total.

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 Post subject: Re: Shallow Madness
PostPosted: Tue Jun 11, 2013 2:32 pm 
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Dave,

Great puzzle with surprisingly few responses!

David Pitcher wrote:
Is the geometry deeper-than-origin-cut, or is it shallow-cut?
Why is the geometry hard to classify? Please show me the cut curve, and I can directly tell you whether that is a shallow cut curve or a deeper-than-origin cut curve. Shape-modding this puzzle into a sphere, or even inverting it and getting the flat faces at the other side of the cut does not change its geometry classification.

The key question is of course whether the two geometrically different versions of this puzzle actually behave differently. For RotoPrism 2 we now know the answer. For Shallow Madness, the jury is still out ...

Oskar

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 Post subject: Re: Shallow Madness
PostPosted: Tue Jun 11, 2013 3:55 pm 
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Beautiful and elegant as always <3

What would a faceturning version look like? You'd get an another trigonal dipyramid with acute angles at the polar vertices, but what would the cuts look like?

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 Post subject: Re: Shallow Madness
PostPosted: Tue Jun 11, 2013 4:12 pm 
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Oskar wrote:
David Pitcher wrote:
Is the geometry deeper-than-origin-cut, or is it shallow-cut?
Oskar wrote:
Why is the geometry hard to classify?
Shallow Madness is not hard to classify, it is a shallow-cut puzzle both geometrically speaking, and in terms of it's cut curve. I was referring to the Deeper Madness puzzle, and the debate regarding it's classification. The jury is indeed still out as to whether a shallow-cut version of that puzzle behaves differently than your original deeper-than-origin-cut Deeper Madness puzzle.

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 Post subject: Re: Edge of Insanity (formerly Shallow Madness)
PostPosted: Thu Jun 20, 2013 12:32 pm 
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As you can see, I have decided to change the name of this puzzle from "Shallow Madness" to "Edge of Insanity". The reason for the change will become apparent when I release my latest puzzle, sometime within the next day or so.

Coaster1235 wrote:
Beautiful and elegant as always <3

What would a faceturning version look like? You'd get an another trigonal dipyramid with acute angles at the polar vertices, but what would the cuts look like?
Thank you for the kind words, and my apologies for taking so long to answer! I'm afraid that I'm not quite sure what you mean by a faceturning version. Can you sketch something out?

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 Post subject: Re: Edge of Insanity (formerly Shallow Madness)
PostPosted: Thu Jun 20, 2013 2:56 pm 
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A crude SketchUp mockup results in this:
Image
It indeed looks like a shallower-cut More Madness, I don't know why I expected to get a 'sharper' dipyramid. I think the cyan pieces are hidden in the Edge of Insanity, though. (Love the new name.)

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 Post subject: Re: Edge of Insanity (formerly Shallow Madness)
PostPosted: Thu Jun 20, 2013 9:58 pm 
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Coaster1235 wrote:
(Love the new name.)
Thanks!

Coaster1235 wrote:
It indeed looks like a shallower-cut More Madness
Yes, the geometry you've draw is a shallower version of More Madness, where the centers of rotation (the axles) become visible, as on a Rubik's Cube. This is moving the slice planes in the opposite direction that they were moved in to create Edge of Insanity, where they have been moved past the origin towards the non-equatorial edges of the puzzle.

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