Sunday, October 11, 2015

More Tessellations: A Coloring Book

Before I continue with posts about Exploring Tessellations: A Journey through Heesch Types and Beyond, I would like to mention a spinoff of that effort. For some of the isohedral classes that have shapeable sides, I had no examples in the collection of designs I used for mazes. For others I had only weak examples. I needed to develop examples that would clearly illustrate each class and show contrasts with other classes. As I finished the book (if in fact I have finished it —I expect I will be making revisions as I discover mistakes and as I learn more—there is so much more to know), I decided to reuse material in the format of a coloring book. The creation of More Tessellations: A Coloring Book was quick and easy compared to the time I have spent on Exploring Tessellations.

The book has the same format as an earlier coloring book of tessellations, A Tessellating Coloring Book. The cover is more attractive and an added feature is that the last page of the book identifies the Heesch type, isohedral class, and symmetry group of the designs used on each page. Three years ago I did not know enough about tessellations and symmetry to do a similar page.

The pages have many pictures of standing birds, though not those previously used in A Tessellating Coloring Book. (For some reason I find birds the easiest motif to tessellate.)

 I was very pleased with finding a bird design for Heesch type CC3C3C6C6.

These birds form a C3C3C3C3C3C3 type tessellation.

I like the abstract appearance of this pattern that on closer inspection is composed of mites (though they do not have enough legs).

IH90 is type CCC with all edges identically formed. It makes a visually appealing pattern

 IH14 is special case of type TTG1G2TG2G1 in which the TT edges are unshapeable straight lines and the four G sides are shaped identically. The right side of the tile is a mirror image of the left side. The illustration shows two ways it can be formed with the same sides. It has cm symmetry.

In a previous post I showed an illustration of class IH9. So far I have not converted it in Fontographer. The coloring book has a different illustration of IH9, shown below.

Some pages have more than one tessellation pattern. In the picture below are
examples of IH71 and IH61. Both patterns have all edges identically shaped, but the way the edges are arranged differs from one pattern to the other.

Here is the finished version of IH18, illustrated earlier while still in Tesselmaniac. It has p31m symmetry.

There is a very limited audience for all the books I have designed. I hope that the few people who eventually buy this one will enjoy it. It is available from CreateSpace and Amazon.

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