Message #1346

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Re: Other 4D puzzles
Date: Tue, 25 Jan 2011 21:47:36 -0800

On 1/25/2011 8:53 PM, Roice Nelson wrote:
>
>
> Great stuff guys!
>
> Special thanks for helping me to picture the nature of a cell-turning
> 24-cell puzzle. In trying to understand the extra cuts you described,
> I see now that they are somewhat related to the incidence
> <http://en.wikipedia.org/wiki/Incidence_%28geometry%29> properties of
> adjacent cells. In particular, the unusual cuts come from
> the adjacent cells with vertex-only incidences. (btw, "parallel to
> vertex" rather than "perpendicular to vertex" seems like decent
> language, though this wording does refer to the adjacent cell the cut
> is based on.) At first I thought the 24-cell puzzle would also need
> cuts parallel to edges, but there are no adjacent cells having
> incident edges which do not also have incident planes. On the
> 16-cell, there are adjacent cells with all three possible incidence
> types, and it looks like there will be three styles of cuts on its
> tetrahedral cells. Both puzzles sound difficult! We’ve never run
> into these kinds of situations before because the adjacent cells on
> puzzles with simplex vertex figures all have incident planes.

Don’s new engine may support the 24 cell but I’m not sure. It’d be good
to check before attempting an implementation.

>
> I also thought I’d mention that I never felt fully comfortable calling
> Magic120Cell a "4D Megaminx", due to some of the analogy ambiguities
> you are discussing.

Is there any other puzzle you can imagine that might deserve that
description? Either way we can certainly say that the Magic120Cell can
easily be considered to be the natural 4D analog of the 3D Megaminx.
That’s my feeling anyway.

> Similarly, my personal preference leans towards not using terms like
> "4D Skewb", unless all could agree on the most defining Skewb-like
> properties. Since a 3D Skewb is a vertex-turning puzzle with slices
> halfway between diametrically opposed vertices, it could be argued
> that the 4D Skewb must have all these properties, with the only change
> being that the properties are now applied to a hypercube (in other
> words, that the 4D Skewb is the puzzle you described that has faces
> that look like Dino cubes). I guess my point is that I prefer
> language like Nan used, explicitly describing the polytope and the
> nature of the twisting. But I also agree the naming is not the most
> important aspect (and I’ve never been good at creating interesting
> puzzle names), so that’s all I will have to say about that :)

Well I share your aesthetic of preferring to let form follow function
here rather than the other way around. I just hope that I’ll be forgiven
if I’m contradicting what I just said about the Megaminx. :-)

>
> P.S. Anyone know where you can buy the face-turning-octahedron puzzle?
> I’d like to own one.

Me too! I don’t know if I ever mentioned this but long, LONG ago within
a year or two of Erno Rubik’s puzzle hit the planet like a virulent
meme, I decided to build a face-turning octahedra. I developed the
ability to combine plaster casts with silicone gel to handle some
concavities in order to cast fiberglass resin pieces. It was such slow
work that I never finished more than about a third of the pieces and a
central hub consisting of bolts with their heads welded to each other.
Not so long ago I decided I was never going to finish it so I threw most
of it away though I think that I kept a few of the cast pieces as they
were quite a lovely translucent amber. I’ve been waiting all these years
expecting it to pop up at some point but it never seemed like anyone was
going to make it. I was glad to see it on GelatinBrain however.

-Melinda

P.S. Please excuse that I truncated the thread history here as it was
getting very long and is archived in the Yahoo group. This is definitely
an interesting thread with lots more to say on the subject.