Message #1178

From: Roice Nelson <>
Subject: Re: [MC4D] Re: Tetrahedral prism {3,3}x{}, 3 layers solved
Date: Tue, 28 Sep 2010 11:52:22 -0500

Hi Andrey and Nan,

Cool to hear about your adventures with the tetrahedral prism puzzles. The
reason the {3,3}x{} puzzles aren’t in the UI is that there were known
problems with them, as you’ve found. Plus, we had to leave some items for
future releases :) I dug up the development emails we were exchanging last
year to refresh my memory, and am including a few relevant portions below.

on 11/11/09, roice wrote:

> So… we have coded a possible change in the sticker twisting behavior and
> are curious of your thoughts compared to the current behavior you just
> tested. The candidate behavior is that all 2C pieces only do "face center"
> twists, all 3C pieces only do "edge" twists, and all 4C pieces "corner"
> twists. 1C pieces wouldn’t twist anything at all. So 2C pieces that are
> very close to a corner would no longer do a corner twist. This change also
> would correct the behavior you noted on the length-7 dodecahedral prism.

on 11/11/09, roice wrote:

> However, I already happened to run into an interesting downside behavior
> with the change. I got the tetrahedral prism puzzles working tonight, but
> held off enabling in the UI just yet because of the following. Similar to
> David’s observation of how the length-2 simplex puzzle has a 5C piece, the
> length-2 and length-3 tetrahedral prism puzzles have a number of stickers
> which should twist like 2C pieces, but actually are part of 4C pieces. So
> the wrong grips get considered, and the end result is some twists which we
> want are being disallowed. The puzzles are therefore unduly limited. In
> fact, on the length-2 puzzle, the end result is that only the two
> tetrahedral faces can be twisted, and the current scrambling code goes into
> an infinite loop because it doesn’t like the lack of variance there.

In short, MC4D currently uses a "piece type" property (2C/3C/4C) to help
control twist types. This is mostly good, but number-of-colors turns out
to not be a discriminating enough property in all situations (in particular,
on the tetrahedral prisms). The problem of matching up pieces with twist
types is a difficult one to find an elegant general solution for. When this
is worked out and these puzzles are officially released, they will likely
have slightly different twisting behavior.

I think it’d be nice to change the relative sizes of the tetrahedra and
prism portions on these puzzles as well. Unlike other polytopes which are
constrained to have fixed cell sizes, prisms have some extra flexibility

Take Care,

On Tue, Sep 28, 2010 at 10:17 AM, schuma <> wrote:

> Congratulations! Nice work!
> Yesterday after seeing you mentioned {3,3}x{}, I tried the 2-layer version
> immediately. For the 2-layer version, any automatic scramble freezes the
> program. So I have to manually scramble it. But all allowed scrambles are
> always trivial to solve.
> Then I went on to see the 3-layer version. I found it not easy and I didn’t
> that ctrl-f work for this version. I should give it a try soon.
> Nan
> — In, "Andrey" <andreyastrelin@…> wrote:
> >
> > It’s strange that one of the smallest 4D puzzles is not listed inMC4D
> puzzle list, so you have to generate it by "Invent my own" command (with
> line "{3,3}x{} 3").
> > It took some time to find the most convenient views of the puzzle (view
> with two tetrahedrons has very different "shrink face" value than view with
> 4 prisms). You can’t rotate prism to 120 deg, so use sequence of two 180-deg
> turns instead. Not very easy…
> > I started with sorting of pieces - top, middle and lower layers (like
> the solver who plays with 3^3 first time - build one single-color face :) ).
> Then there was orientation of middle layer pieces and then combining of 3rd
> layers parallel to prisms (just 3-cubie segments) with adjacent cubies. Next
> step was to put all corners in their place - and there were first two
> problems.
> > First, middle layer was upside-down - and I had to flip all its pieces
> and save colors of top and bottom faces.
> > Second, in the end of this stage I found one corner piece (pair of
> pieces, really) with wrong orientation! It is normal for pyraminx, but here
> you have to think how it can be :)
> > When all corners ans 3Cs of middle layer were in place I found myself
> with 3 parallel pyraminxs and with the task to put all their 2Cs in place.
> > One operation was enough for it… well, almost enough. At first I
> tried to move cubies to places in proper orientation, but soon found that I
> can’t remember setup twists that contain of pairs of prism flips… So I
> decided to position pieces first.
> > Solving of 3 pyraminxs with the same sequence of 3-cycles went
> smoothly… until there were two transpositions on opposite faces (parity
> problem?). When I solved it there was one wrong oriented cubie on top side
> (and 3 on bottom) - but this time I could remember setup twist ))) So when I
> twisted 3 sets of 2 cubies, puzzle was almost solved.
> > So this one is solvable from the scratch, without operations
> development. It doesn’t beat {3}x{3},3 :)
> >
> > Andrey
> >
> ————————————
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