# Message #2006

From: Roice Nelson <roice3@gmail.com>

Subject: Super Puzzle Sunday!

Date: Sun, 05 Feb 2012 18:26:09 -0600

Hi all,

When I wrote last, MagicTile had 63 puzzles configured. *Now it has over

450!* Here are some highlights:

- 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. - 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! - Hemispherically sliced puzzles for all the other platonic solids too

(though the labels end up being different for the different shapes). - {3,6} and {4,4} Klein Bottles<http://en.wikipedia.org/wiki/Klein_bottle>.

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 - Analogues of Pyraminx Crystal and other Dodecahedral slicings, but on

the {6,3} tilings. - Many new FT {7,3} puzzle cut depths.
- 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. - 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. - 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. - Three strange {8,4} colorings. It would be a fun mini-project to do

analysis of the topological structure of these. - *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<br>
Q is the number of incircles<br>
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