Message #1940

From: Roice Nelson <roice3@gmail.com>
Subject: new {5,4} puzzles
Date: Sun, 27 Nov 2011 18:57:51 -0600

Hi all,

I added some fun {5,4} puzzles. With cells identified, the tiling for
these new puzzles has a checkerboard pattern with *only two* colors.

The FT version is trivial because a twist does not change the puzzle state,
so I didn’t include it.

The ET version is enjoyable, even if not very difficult. A
checkerboard<http://groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/pic/39707321/view>
of
the stickers is easy to make on this puzzle.

I haven’t figured out the VT versions, but they seem pretty coupled and
should be more difficult. Here is something unusual about them… Each
slicing circle is "double covered". The identified vertices of two adjacent
cells (of a given color) are at the same location, so there are really two
overlapping circles there. The puzzle still makes sense when twisting
because of the checkerboard color pattern around vertices.

For some time now, there have already been 6-color and 12-color puzzles
based on the {5,4} tiling. The 6-color is non-orientable, the 12-color
orientable, and the patterns of both are strange. I don’t think those
colorings can be used as a basis for a {5,3,4} periodic painting, which we’ve
wondered about in the past
here<http://games.groups.yahoo.com/group/4D_Cubing/message/1014>,
because
the coloring does not remain the same after a 1/5th rotation of the entire
plane. I hope I’m wrong, but I suspect that the maximal coloring for the
{5,3,4} has just two colors. However, VT and ET puzzle versions of that
honeycomb would still be very neat to see.

Cheers,
Roice