Message #1450

From: Roice Nelson <>
Subject: slicing up MagicTile puzzles without triangle vertex figures
Date: Tue, 22 Feb 2011 22:18:57 -0600

Hi all,

I made a toy to help study the problem of how to slice up (face turning)
MagicTile puzzles that do not have triangle vertex figures, and wanted to
share. Honestly, my initial impression is that I wish the slicing turned
out to be more elegant in the general case. Instead, there seem to be a
huge number of possible puzzles for tilings like the {3,7}, none of them
which feel particularly natural to me. You can play with the study tool
directly in a web browser if you have Silverlight installed (or are willing
to install it). I seem to be overtaxing the Silverlight drawing a bit, and
some of the spherical puzzles aren’t perfect due to things projecting to
infinity, but it serves the purpose I wanted pretty well.

Here are a few thoughts I had, but I’d really love other opinions on what
would be the best puzzles for the next iteration of MagicTile.

I can capture pictures of some of the above if people need, but hopefully
you are able to play with it directly to follow what I’ve written. I
couldn’t picture this stuff very well ahead of time myself, without seeing
it in motion.

Anyway, I’m curious what puzzles people would like to see actualized, if
any. Are there any slicing options which feel particularly natural to you
on any of the tilings? Would people even attempt to solve them? (In other
words, are they worthwhile to spend time creating?)