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 Post subject: Shallower Madness
PostPosted: Thu Jun 20, 2013 2:29 pm 
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Location: Boston area
Hi Everyone,

I'm pleased to introduce my latest puzzle, Shallower Madness. As you might guess, this puzzle is in the "Madness" series of puzzles started by Oskar. In fact, this puzzle looks nearly identical to Oskar's Deeper Madness puzzle. What makes this puzzle different is that I've used shallow cuts and a shallow cut-curve internally. You may recall that Oskar's puzzle uses a deeper-than-origin cut curve. The difference in the two puzzles becomes clear once you start trying to scramble them. Hopefully the video will explain things sufficiently:

VIDEO

Interestingly, there are many situations on Shallower Madness where axes appear to be available, but are internally blocked. This is similar to Deeper Madness, but there are many more blocked axes with Deeper Madness. Does anyone know the answer to my question in the video?

I was not going to sell this puzzle since it looks exactly the same as Oskar's, and since it does pop apart easier than I like my puzzles to do (although as you can see in the video, it is perfectly playable). However, at Oskar's request I am making Shallower Madness available for sale in my Shapeways shop: Shallower Madness

Here are some pictures of Shallower Madness:
Attachment:
Shallower Madness Solved.JPG
Shallower Madness Solved.JPG [ 195.77 KiB | Viewed 956 times ]
Attachment:
Shallower Madness Mid-Turn.JPG
Shallower Madness Mid-Turn.JPG [ 203.58 KiB | Viewed 956 times ]


Here are a few pictures of Shallower Madness next to Deeper Madness, showing some places where Shallower Madness can turn, but Deeper Madness cannot. In each picture Shallower Madness is in mid-turn on an axis not available to turn on Deeper Madness:
Attachment:
Shallower Madness & Deeper Madness.JPG
Shallower Madness & Deeper Madness.JPG [ 229.83 KiB | Viewed 956 times ]
Attachment:
Blocked Turn 1.JPG
Blocked Turn 1.JPG [ 201.56 KiB | Viewed 956 times ]
Attachment:
Blocked Turn 2.JPG
Blocked Turn 2.JPG [ 222.66 KiB | Viewed 956 times ]
Attachment:
Blocked Turn 3.JPG
Blocked Turn 3.JPG [ 181.76 KiB | Viewed 956 times ]


Many thanks to Oskar for his encouragement in making this puzzle, and for sending me the Deeper Madness puzzle so that I could conduct this bit of twisty science!

Have fun!
Dave

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 Post subject: Re: Shallower Madness
PostPosted: Thu Jun 20, 2013 2:58 pm 
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Hi Dave,

Wow, fascinating analysis and comparison!

I had already suspected that Deeper Madness does not scramble very well. Of course, we could do some internal unbandaging. I managed to internally unbandage More Madness to an extent that it has no internal bandaging anymore. I tried to do the same for Deeper Madness, but failed.

Here is your next challenge: design a Shallower-Madness-Without-Any-Internal-Bandaging :-)

Oskar

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 Post subject: Re: Shallower Madness
PostPosted: Thu Jun 20, 2013 3:40 pm 
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Congratulations Dave, :)
What is the difference between this one and the Shalow Madness puzzle?

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 Post subject: Re: Shallower Madness
PostPosted: Thu Jun 20, 2013 3:58 pm 
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Location: Finland
The Shallower Madness loses one piece type (the edge in the non-equatorial edges) and gains two piece types (the small edge in the equatorial edges and the chiral triangles next to it).

By the way, are the equatorial vertices four-fold? As in, is the angle between two equatorial edges the same as the angle between two non-equatorial edges that meet in an equatorial vertex? If they are, then all the dihedral angles are equal. So I might as well ask: are all the dihedral angles equal? Is that what defines the special 'madness' tripyramid?

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 Post subject: Re: Shallower Madness
PostPosted: Thu Jun 20, 2013 9:55 pm 
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Location: Boston area
pooya13 wrote:
What is the difference between this one and the Shalow Madness puzzle?
I've renamed Shallow Madness to Edge of Insanity to avoid confusion with this puzzle. But to answer your question, the difference is that Edge of Insanity has the slice planes moved closer to the edges. This makes all of the pieces (except the core) visible, so with Edge of Insanity there is no internal blocking. Due to this I found Edge of insanity to be much easier to scramble, but it is still a very difficult puzzle that is not at all obvious how to solve.

Coaster1235 wrote:
are all the dihedral angles equal? Is that what defines the special 'madness' tripyramid?
Yes, they are equal, and that is what makes this particular trigonal dipyramid special. This same shape is seen in Fracture-6, Sunrise Sunset, More Madness, and other puzzles.

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 Post subject: Re: Shallower Madness
PostPosted: Thu Jun 27, 2013 9:21 am 
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David Pitcher wrote:
Does anyone know the answer to my question in the video?
Since this question has been answered on YouTube, I'll show a few more pictures here that demonstrate the scrambling ability of Shallower Madness:
Attachment:
Shallower Madness Scrambled.JPG
Shallower Madness Scrambled.JPG [ 167.08 KiB | Viewed 684 times ]
Attachment:
Shallower Madness Scrambled 2.JPG
Shallower Madness Scrambled 2.JPG [ 203.55 KiB | Viewed 684 times ]
Attachment:
Shallower Madness Scrambled 3.JPG
Shallower Madness Scrambled 3.JPG [ 170.03 KiB | Viewed 684 times ]


As you can see, Shallower madness can become quite thoroughly scrambled.

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