Fun stuff so far. One big revelation has been the parallel between simple groups and prime numbers. I'm still a bit unclear on the concepts -- so I will struggle to explain them properly and clearly.

Classification of finite simple groups - Wikipedia, the free encyclopedia:

The classification of the finite simple groups, also called the enormous theorem, is believed to classify all finite simple groups. These groups can be seen as the basic building blocks of all finite groups, in much the same way as the prime numbers are the basic building blocks of the natural numbers. The Jordan-Hölder theorem is a more precise way of stating this fact about finite groups.

List of finite simple groups lists the 26 simple finite groups, including the famous Monster group.

Reading the book has made me look at the bathroom tiles, to notice that all the tiles are of one type -- and that you just need to rotate them.  What symmetry group is embodied by the tiles?  Is the vast majority of commerical household tiles of the same group?

When did people start making tiles?

What is quasi-periodicity?

How does symmetry show up in textiles? I'm working through understanding List of planar symmetry groups - Wikipedia, the free encyclopedia