Message #2175

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Re: Making a puzzle based on 11-cell
Date: Wed, 23 May 2012 15:29:29 -0500

This is fantastic Nan!

I really like your design choice for displaying the core colors. It is
especially lovely how clean the pristine state looks.

It looks fair to say this is a "cell turning" 11-Cell. For twisting a
cell, would it be difficult to also include twisting the cell around an
edge? In addition to giving full cell-turning functionality, this would be
helpful to see how the 3C edges connect up.

On the 3^4, you can do 3C/4C twists, then solve them with 2C twists. The
situation here is analogous. You can do a single 6C twist, then solve it
with three 2C twists. It’s a good bite-sized challenge to try! I don’t
know yet if you can do a single 2C, then solve with 6C twists. That will
be a fun question to reason through.

I realize the slicing is abstract (topological vs. geometric). I think
it’d be nice to make the size of the 3C/6C pieces bigger, maybe even
controllable with a slider or something. This would make the puzzle feel a
little more like a classic Rubik’s Cube.

Not a big deal, but I think it’d be better if puzzle reorientations did
not increment the move count.

My brief experience with this makes me wonder about a "vertex turning"
11-cell as well. Overcoming the hurdle of how to make twists on a VT
puzzle seems especially difficult (even more so than it was for the
polychora puzzles).

Great work! It’s awesome to see permutation puzzles enter the domain of
abstract polytopes, and I look forward to studying this more :D

Cheers,
Roice

On Tue, May 22, 2012 at 9:50 PM, schuma <mananself@gmail.com> wrote:

> Hi guys,
>
> In the last week I’ve been working on the 11-cell. Although not completed,
> it’s a playable puzzle now. I’ll keep refining it. But I want to let you
> guys see the current version of the applet:
>
> http://people.bu.edu/nanma/ElevenCell/ElevenCell.html
>
> When you open it, you can see eleven hemi-icosahedral cells. The color
> scheme is exactly identical to the one here: [
> http://en.wikipedia.org/wiki/File:Hemi-icosahedron_coloured.svg]. But in
> that figure, the faces are colored to be identical to the opposite cell,
> whereas in my illustration, the faces are colored to be identical to the
> cell it belongs to. I also changed the layout of the cells to make it more
> intuitive.
>
> There are 11 cells. I consider each cell has a core that never moves. The
> core is represented by a colored disk as the background of a cell. Just
> like the centers of the Rubik’s cube, the cores should be used as
> references during a solve. There are 2-color face pieces, 3-color edge
> pieces, and 6-color vertex pieces. When you move the cursor on a cell, the
> turning region will be highlighted. The region includes all the pieces that
> have stickers on the hemi-icosahedron.
>
> Left or right clicking the mouse will twist the puzzle. I’m allowing
> twists around vertices and face centers. When the cursor is on top of a
> vertex, all the stickers on the vertex piece will be circled. When the
> cursor is on top of a triangular face, the two stickers on the face piece
> will be circled. These features can help you see the connectivity of
> 11-cell, to some extend. Please try click on the red cell, which is
> considered by myself as the "central cell". Twists around that cell are
> more symmetrical and thus understandable.
>
> Holding shift and clicking mouse will re-orient the whole puzzle.
> Currently this is the only way to re-orient.
>
> The checkboxes "F", "E", and "V" controls the visibility of the faces,
> edges and vertices. The percentages of stickers in the correct position are
> also shown. When all are solved, the background turns light blue.
>
> The meaning of the buttons "reset" "scramble" and "undo" are
> self-explaining. I put a "1-move scramble" button for testing purpose. But
> I found it was already a nontrivial challenge. Let me know if you can solve
> it!
>
> In the future I will fix bugs, and add macros. I haven’t seriously thought
> about how to solve it. But it looks like a pretty deep cut puzzle: each
> turn affects six out of eleven vertices, and it should be hard to solve. So
> I think macros should be necessary.
>
> Nan
>