Message #1455

From: schuma <mananself@gmail.com>
Subject: Re: slicing up MagicTile puzzles without triangle vertex figures
Date: Sat, 26 Feb 2011 08:03:27 -0000

Hi,

After playing it for a while, I found it a great tool to explore puzzles. Thank you for sharing it. It’s similar in spirit to Jaap’s applet:

http://www.jaapsch.net/puzzles/sphere.htm

But Roice’s handles more general geometries other than only the sphere.

(1) In {4,4}, when the size of circles is right, and only two circles are allowed to rotate, you get a real puzzle: Rashkey
http://www.jaapsch.net/puzzles/rashkey.htm
which is a neat and hard puzzle to solve.

(2) Roice said:
> - On the {3,6}, if you make the circles larger than the parent cell, you can
> slice into 3-per-side by making the slicing circle go 2/3rds the way across
> some adjacent cell edges (which simultaneously puts it 1/3rd the way across
> some incident cell edges). This feels like a nice puzzle to me, with a
> pretty star pattern in the middle of each cell. You can do the same thing
> on the {3,5} icosahedron, but in that case, the cuts are not evenly spaced
> along an edge and the star patten is not quite as regular.

This way of slicing {3,5} should be precisely Gelatinbrain’s (2.1.4):
http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/icosa_f1.gif

(3) In {5,5}, when I increase the size of circles close to the maximum value, suddenly all the cuts jump to the outside of the hyperbolic plane…… Is there a particular reason or just a bug?

(4) Roice said:
> - There is a very cool midpoint slicing of the {3,4}. The doubled-up
> slicing circles form a cuboctahedron, so this is a case where things do fit
> together quite nicely.

This puzzle is the Skewb Diamond (a shape mod of Skewb). It’s interesting that it can be viewed as a cuboctahedron.

(5) A {6,3} puzzle with large circles is simulated by Gelatinbrain (7.1.1, 7.1.2, 7.1.3, with different repeating patterns).

In general, I’d like to see some of the puzzles of this kind, especially in the hyperbolic plane. Since there is no macro function, I don’t think I can solve puzzles with too many small pieces. Brandon, I’m not that crazy…

Nan