Message #1911

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Re: {7,3} vertex and edge turning puzzles
Date: Tue, 08 Nov 2011 17:45:36 -0600

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@superliminal.com>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?
>