Wednesday, July 18, 2018

Further maze book revisions

After updating tessellating maze books in May, I updated some other books. While doing that I discovered patterns that made simple mazes quite difficult to solve. I could not resist the temptation to include some and so did a second round of revisions and updating. Below is a sample, though not an actual maze from either book. All the paths go through the corner swirls.
The updating resulted in the elimination of a number of common geometric tessellations that, while they made decent mazes, were not of much interest to those looking for visually-interesting tessellation. Tantalizing Tessellating Mazes had four additional pages changed and More Tessellating Mazes had 12 additional pages changed. As a result of the two 2018 revisions, both books have 39 new mazes and 45 holdover mazes.

In the maze above there are two shapes that tessellate. The top one is an example of isohedral class IH71. All edges are shaped the same and there is mirroring over a diagonal line. The bottom shape is an example of class IH61. The tile has two-fold rotational symmetry and uses the same edge as the top shape.

(If the maze above is presented with big openings through the sides rather than the little openings through the curved corners, it is trivially easy to solve. See below.)

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