Message #1915

From: schuma <mananself@gmail.com>
Subject: Re: {7,3} vertex and edge turning puzzles
Date: Wed, 09 Nov 2011 23:16:58 -0000

Today I visited MSRI to see this sculpture of the Klein Quartic
<http://groups.yahoo.com/group/4D_Cubing/photos/album/1962624577/pic/167<br> 5084071/view> . The base is a {7,3} in the Poincare Disk view just like
in Magic Tile. The main part of the sculpture is a folded version of it,
which has 24 curved heptagons.

Nan

— In 4D_Cubing@yahoogroups.com, "schuma" <mananself@…> wrote:
>
> Maybe another possibility is to use ceased heptagons, just like this
one:
>
> <http://westy31.home.xs4all.nl/Geometry/KleinHoles.jpg>
>
> This photo is from a long webpage by Gerard Westendorp. If you go to
<http://westy31.home.xs4all.nl/Geometry/Geometry.html#constant> and
scroll UPWARD a little bit, you can find the discussion about it where
he considered different ways to "glue" the cardboard model. One way
results in Klein Quartic. Another way results in the dual of the {3,7}
IRP that we have in MagicTile. There are even more ways resulting in
other {7,3} with other connectivity. I need to catch up on math but it
looks interesting.
>
> Some experience about solving IRP puzzles:
>
> I’ve solved three simple IRP puzzles. For each of them, I solved it in
two ways: the "show as IRP" option true and false. I found solving in
the IRP view more challenging than in the Poincare disk (PD) view,
because (1) in PD I can see everything but in IRP I can only see about
half; (2) in IRP the pieces with best visibility are on boundary, but
some of them are truncated; (3) when I’m making a turn sometimes the
face that I need to click on is facing the other direction. Sometimes I
have to carefully adjust the viewpoint and click on some inside faces.
Because of the above reasons, I always first look at the puzzle with the
IRP view off to study it, before turning on the IRP.
>
> Nan
>
>
> — In 4D_Cubing@yahoogroups.com, Roice Nelson roice3@ wrote:
> >
> > That’s a really creative idea. When I first saw your suggestion, I
had the
> > same question as Nan.
> >
> > MagicTile can’t support this with only via configuration at the
moment. It
> > will take some code work, but I like the thought of trying to handle
it in
> > the future.
> >
> > Like the {3,7} puzzles, my bet is this IRP puzzle will not have the
same
> > connection pattern between heptagonal faces that the current KQ
puzzle has.
> >
> > A further speculation is that although there might not be a {7,3}
IRP that
> > fits into *R**3*, maybe there is one that fits into *R**4 *or
something
> > else. In any case, I wouldn’t be surprised if there is a different
set of
> > 2-dimensional IRPs that can work in 4-dimensional space, in a
similar way
> > to the ones Melinda has enumerated for 3 dimensions.
> >
> > Roice
> >
> >
> > P.S. Short implementation thoughts, probably just for me…
> >
> > A longer term goal is to support truncated tilings (giving puzzles
based on
> > uniform tilings, etc.). I’m not sure how it is going to evolve
exactly, but
> > one approach would be to still have one texture mapped to each
polygon in
> > the underlying regular tiling. It’d just be that the texture now
contained
> > portions from multiple tiles instead of just one (e.g., a soccer
ball
> > puzzle would have 32 faces, but only 20 textures). The {7,3} IRP
could
> > potentially fit well into that piece of work. What I’m thinking is
that the
> > code would handle this as a {3,7} tiling that is truncated all the
way to
> > its dual.
> >
> > Maybe the right solution for truncated tilings is still one texture
per
> > face though, in which case this IRP could be harder to do…
> >
> >
> > On Tue, Nov 8, 2011 at 1:03 AM, Melinda Green melinda@wrote:
> >
> > > No, I was inquiring into the possibility of such a puzzle. I meant
to
> > > send privately to Roice because I didn’t want to pressure him but
I
> > > screwed up.
> > >
> > > I’m pretty sure there isn’t a true {7,3} IRP though I hope that I
am
> > > wrong. I could however imagine a MagicTile version in which a
{7,3}
> > > texture could be mapped onto the VT {3,7} IRP surface to
approximate
> > > one. Seems doable though the real way to do this sort of thing
might be
> > > to map it onto a minimal curvature surface with the same topology.
The
> > > IRPs are interesting because they can be constructed using flat
> > > polygonal faces but there are all sorts of crazy puzzles that
become
> > > possible without that constraint.
> > >
> > > -Melinda
> > >
> > > On 11/7/2011 10:50 PM, schuma wrote:
> > > > Is there a {7,3} IRP?
> > > >
> > > > — In 4D_Cubing@yahoogroups.com, Melinda Green<melinda@>
wrote:
> > > >> How about a FT {7,3} IRP?
> > >
> >
>