Message #2826

From: Roice Nelson <roice3@gmail.com>
Subject: Re: Re: [MC4D] RE: New puzzles
Date: Tue, 19 Nov 2013 01:12:18 -0600

ok, we’ll do them as separate puzzles then. I won’t repeat the
face-turning slicing in both places though, since the face-turning versions
will behave identically. Would be nice if we can come up with some
distinguishing naming too.

I’m not sure I followed your last question. Did you mean to ask if you can
do an identification with an "in place reflection" and "end rotation", but
without extra *reflections*? If that is what you meant, this is possible
to configure, though I’m not sure it can lead to sensical topologies. I
just tried it on a couple puzzles including the {8,4} 9C and only achieved
strange results, but maybe there is some case where it would work. To have
no reflections, use the same trick I suggested above and make the EdgeSet

1. Internally, this reflects the tile twice, but the second reflection
   just undoes the first one. You can do this and set the other properties
   however you want.

{8,4} 9C has 9 faces, 16 edges, and 8 vertices, so the Euler Characteristic
is 1 and the topology is the projective plane. As configured, there are
some vertices and edges that look identical (same colors) but are
physically different. Not all the faces are octagons. Looks like 4 are
squares and 4 are digons. It is a strange puzzle for sure.

Roice

On Mon, Nov 18, 2013 at 1:48 PM, <andreyastrelin@yahoo.com> wrote:

>
>
> Roice,
>
> I think, it’s better to add new puzzles with additional identifications
> on vertex- and edge-centered twists. Because they are really different
> puzzles, and some of them may be much more difficult than old ones.
>
> I’m looking at {8,4} 9 colors, and can’t understand it. In
> face-centered puzzle it works like non-oriented non-uniform puzzle with
> some two-side edges. In vertex-centered variant some vertices of the same
> structure are identified, but sometimes there is only half of them… and
> the identified ones don’t all have the same orientation.
>
> Is it possible to add identification with "in place reflection" and "end
> rotation", but without extra rotations?
>
>
> Andrey
>
>
> —In 4D_Cubing@yahoogroups.com, <roice3@…> wrote:
>
> Hi Andrey,
>
> Thanks for your observation about this. To get the "mathematically pure"
> behavior you are wanting, we can add an additional identification to each
> of these puzzles, one that is a rotation only (no reflections). We can
> effectively get that by marking EdgeSet 0, and using the appropriate
> EndRotation… 4 for {8,3} and 5 for {10,3}.
>
> Because of the solutions listed in the table, there is the question of
> whether to edit the existing puzzles or add new ones. The existing
> definitions are valid configurations too, just with a different topology.
> But they are similar enough that I’m thinking we wouldn’t want separate
> definitions with only this difference.
>
> If it is ok with you and others, I will just change the behavior of the
> existing puzzles and not worry about the table, but if anyone disagrees
> please let me know. I’ll push the change out at the same time as the
> addition of all the new colorings you’ve been making.
>
> Thanks again,
> Roice
>
>
>
> On Sun, Nov 17, 2013 at 3:22 PM, <andreyastrelin@…> wrote:
>
>
>
> Roice,
>
> something is wrong with {10,3} 6C edge-rotated puzzles. When I select
> some edge, I expect that edges on opposite sides of its decagons will be
> selected too (because mathematically they are the same). But that edges
> remain non-selected. Same is true for vertex-rotated 6C, and also for
> {10,3} 12color.
>
> Is there something missing in puzzle description?
>
>
> I see the same in {8,3} 6C… and I don’t like it because there are
> solutions of these puzzles in the table (including some of my own ones)…
> Looks like we solved puzzles that are not as "mathematically pure" as they
> should be.
>
> Andrey
>
>