# Message #1459

From: Matthew <damienturtle@hotmail.co.uk>

Subject: [MC4D] Re: slicing up MagicTile puzzles without triangle vertex figures

Date: Sun, 27 Feb 2011 00:33:06 -0000

I’ve had some fun with the slicing program, it makes some pretty shapes and patterns. I would love for arbitrary slices which can be created to be playable as puzzles, though this would probably be a lot of work to implement. One thought I have is that Jaap’s Sphere also allows slices parallel to the faces of a rhombic dodecahedron to be used, equivalent to the edges of a cube/octahedron (similarly for the triacontahedron), and maybe interesting puzzles could be created by a similar means for hyperbolic tilings, by rotating about edges. Another is to use the "fudging" concept (see http://www.shapeways.com/model/204721/futtminx.html?gid=ug13603 for one example, though the idea is a little different here) started by Oscar van Deventer to tweak the geometry and remove small pieces if so desired, if any ideas from this are implemented. No doubt people like Brandon and Nan will have no problems with these small pieces though.

— In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@…> wrote:

> Thanks for telling me about the Skewb Diamond. With the sizing newly

> available on the spherical puzzles, I see now you can do something analogous

> with the {5,3}. The midpoint slicing that doubles up slicing circles

> results in a circle set that is an icosidodecahedron (looks like this is the

> "Pentultimate"). The result on the dual {3,5} looks a little stranger,

> having some hexagonal facets (It’s pretty to have both these turned on at

> the same time). I don’t know what shape the latter is, but it’s not in

> wiki’s list of Archimedean solids, so maybe those hexagons aren’t regular or

> are skew or something.

2.1.5 in Gelatinbrain shows the result for the {3,5}, although 1.2.9 may be easier to follow as in the dual shape of the {5,3} it looks identical to a megaminx, the hexagons corresponding to the corners there, if that result helps any. The applets don’t seem to be loading for me just now, so I apologise if I mention the wrong puzzles, but the result is the same.

Matt