Message #1784

From: Roice Nelson <roice3@gmail.com>
Subject: Infinite Regular Polyhedra Puzzles
Date: Tue, 14 Jun 2011 01:18:02 -0500

Hi all,

I’m excited to share some new puzzles based on Melinda’s "infinite regular
polyhedra" (IRP) work. Please visit her
page<http://www.superliminal.com/geometry/infinite/infinite.htm>on
these generalized polyhedra for background. The new puzzles will show
in
the puzzle menu in the latest build of MagicTile (click to
download<http://www.gravitation3d.com/magictile/downloads/MagicTile_v2_Preview.zip>
).

Each puzzle has both an IRP and a Poincare Disk view (which share the same
topology), and you can toggle between the two views at any time via a new
setting. One lovely thing about the IRP puzzles is that they feel more like
working with a traditional 3D puzzle, though they are still by no means
traditional! {3,7}, {4,6}, and {5,5} variants are available to start with,
and I’ve placed a few screenshots
here<http://groups.yahoo.com/group/4D_Cubing/photos/album/793135570/pic/list?mode=tn&order=ordinal&start=1&dir=asc>
.

If you study the new {3,7} enough, you’ll discover it is slightly different
than the Klein Quartic version. It has 56 colors, but in order to map to
the IRP, the pattern of connections between faces is new. However, it will
still be just as difficult a permutation puzzle, so if you’d prefer to work
with the IRP representation, my offer still stands to send a crystal cube to
the first solver of all three {3,7} puzzles. It doesn’t matter if you
choose to use the KQ or the IRP versions.
I want to say thanks to Melinda for exposing me to these objects, for
studying them and creating accessible data files in the first place, and for
helping me get past various hurdles when trying to incorporate them into
MagicTile.

More IRP puzzles will surely trickle out over time too :)

Cheers,
Roice