Message #2011

From: Eduard Baumann <baumann@mcnet.ch>
Subject: Re: [MC4D] Super Puzzle Sunday!
Date: Tue, 07 Feb 2012 13:48:40 +0100

This marvelous MagicTile runs only on one (not the modernst one) of my three PC’s.
Do you know a link for downloading a FBO driver?

Kind regards
Ed

—– Original Message —–
From: Roice Nelson
To: 4D_Cubing@yahoogroups.com
Sent: Monday, February 06, 2012 1:26 AM
Subject: [MC4D] Super Puzzle Sunday!

Hi all,

When I wrote last, MagicTile had 63 puzzles configured. Now it has over 450! Here are some highlights:
a.. Tetrahedron puzzles: Projecting the tetrahedron out to the sphere results in large curvature of faces, so there are some genuinely new puzzles here (which have no corresponding GelatinBrain applet). Check out the ET puzzles in particular.
b.. Dodecahedron and Icosahedron: Added FT and VT hemispherically sliced puzzles (BigChop-like). These puzzles have "1:1:1" labels. I also added crazy versions mixing all three BigChops into one FEV SuperChop puzzle. Very pretty, but must be difficult!
c.. Hemispherically sliced puzzles for all the other platonic solids too (though the labels end up being different for the different shapes).
d.. {3,6} and {4,4} Klein Bottles. And the great thing about Klein Bottles for this group is that they require 4 dimensions to represent the compact surface without self intersections :D
e.. Analogues of Pyraminx Crystal and other Dodecahedral slicings, but on the {6,3} tilings.
f.. Many new FT {7,3} puzzle cut depths.
g.. A class of mixed ET+VT puzzles that apply to various tilings. The edge turning circle size is set to the incircle of the tiling, and the vertex turning size is set to the circumcircle, making all slices intersect at tile centers. The labels of this class of puzzles are "E0:1:0 V0:0:1". On every single spherical puzzle, the initial projections have slices that appear as lines, and I found the Cube and Octahedron projections especially striking. These look nice on {p,q} tilings when q is larger than p, since the edge circles become comparatively smaller - besides the Octahedron, see the {3,5} and {3,7} for instance.
h.. A class of mixed FT+VT puzzles, "F0:1:0 V1:0:0". Slicing circles all intersect at edge midpoints, and it seems like these puzzles should generally be easy.
i.. Check out the {5,5} FEV puzzles. Since it is a self-dual tiling, the slicing around faces and vertices is congruent. Very cool looking, and I bet these are fun to solve.
j.. Three strange {8,4} colorings. It would be a fun mini-project to do analysis of the topological structure of these.
k.. Just lots and lots and lots of new slicing in general, so have a look around.
I tried to select puzzles that have reasonable looking slicing, though perhaps pushed the boundaries of that in a some cases. Maybe some are too difficult or too easy. If you find puzzles that you feel shouldn’t belong, I’d appreciate feedback on that. I welcome suggestions for further slicing too.

In case you are wondering, here is the meaning of the puzzle labels. I wanted to have something auto-generated that gave insight into the depth of the cuts. Hopefully it is terse enough. A slice is displayed with the turning type, "F", "E", or "V", plus a cut diameter specified by three numbers in the form "P:Q:R".

P is the number of tiling edge lengths
Q is the number of incircles
R is the number of circumcircles

These numbers are based on the side lengths of the fundamental p.q.2 triangle of the tiling. P is the side opposite the π/p angle, Q the side opposite the π/q angle, and R the side opposite the π/2 angle (R is the hypotenuse of fundamental triangle). The final slicing circle radius is set to some linear combination of these three lengths. This approach allows you to make much simpler looking expressions for cut depths. I tried to avoid decimals when possible.

There is a new puzzle tree so you can more easily select puzzles, but I still left in the onerous nested menus. This latest version also fixes some bugs I’ve run across. I won’t detail those here, but I encourage you to download the latest rather than use previous versions.

Some things I haven’t done, but would like to do: I should probably add a description of the labels directly in the program, maybe even a visual one. I’d also like to add preview pictures for all the puzzles, to make it easier to see what they look like without actually having to build them.

One last thing: I have removed the "Preview" label :)

www.gravitation3d.com/magictile/downloads/MagicTile_v2.zip

Cheers,
Roice