Reddit reviews The Symmetries of Things

Your post has too little context/content for anyone to give you particularly relevant or specific advice. You should list what you know already and what you’re trying to learn. I find it’s easiest to research a new subject when I have a concrete problem I’m trying to solve.

But anyway, I’m going to assume you studied up through single variable calculus and are reasonably motivated to put some effort in with your reading. Here are some books which you might enjoy, depending on your interests. All should be reasonably accessible (to, say, a sharp and motivated undergraduate), but they’ll all take some work:

(in no particular order)
Gödel, Escher, Bach: An Eternal Golden Braid (wikipedia)
To Mock a Mockingbird (wikipedia)
Structure in Nature is a Strategy for Design
Geometry and the Imagination
Visual Group Theory (website)
The Little Schemer (website)
Visual Complex Analysis (website)
Nonlinear Dynamics and Chaos (website)
Music, a Mathematical Offering (website)
QED
Mathematics and its History
The Nature and Growth of Modern Mathematics
Proofs from THE BOOK (wikipedia)
Concrete Mathematics (website, wikipedia)
The Symmetries of Things
Quantum Computing Since Democritus (website)
Solid Shape
On Numbers and Games (wikipedia)
Street-Fighting Mathematics (website)

But also, you’ll probably get more useful response somewhere else, e.g. /r/learnmath. (On /r/math you’re likely to attract downvotes with a question like this.)

You might enjoy:
https://www.reddit.com/r/math/comments/2mkmk0/a_compilation_of_useful_free_online_math_resources/
https://www.reddit.com/r/mathbooks/top/?sort=top&t=all

I really like this book.

https://www.amazon.com/Symmetries-Things-John-H-Conway/dp/1568812205/ref=sr_1_1?s=books&ie=UTF8&qid=1493910460&sr=1-1&keywords=symmetries+of+things

The classification of wallpaper patterns:

http://www.amazon.com/The-Symmetries-Things-John-Conway/dp/1568812205

Perhaps this or this.

Check out this list. It includes most if not all books mentioned here.

From more to less advanced, generally:

• Geometry by Gray, Esplen, and Brannan
  
  
• The Infinite in the Finite
  
  
• A Geometrical Picture Book
  
  
• 99 Points of Intersection: Examples-Pictures-Proofs
  
  
• Lines and Curves: A Practical Geometry Handbook
  
  
• The Heart of Mathematics
  
  
• The Symmetries of Things
  
  
• A Mathematical Gift, 1: The Interplay Between Topology, Functions, Geometry, and Algebra (Mathematical World) (v. 1)
  
  A Mathematical Gift, II
  
  A Mathematical Gift, III: The Interplay Between Topology, Functions, Geometry, and Algebra (Mathematical World) (v. 3)
  
  Note the first three volumes are cheaper as a set.
  
  Intuitive Topology (Mathematical World, Vol 4)
  
  Groups and Symmetry: A Guide to Discovering Mathematics (Mathematical World, Vol. 5)
  
  Knots and Surfaces: A Guide to Discovering Mathematics (Mathematical World, Vol. 6)
  
  
• A Beginner's Guide to Constructing the Universe
  
  and 5 activity books in the same style
  
  
• Going beyond books, but visual, manipulative, and tactile, the Zome Tools

That reminds me of a book that could be perfect for a course like this:

http://www.amazon.com/The-Symmetries-Things-John-Conway/dp/1568812205/

It discusses the idea of symmetry in great mathematical depth, but in a way that is much less formal and pedantic than a traditional math text. For me, there is something beautiful in the extraordinary variety available in the forms of symmetry explored in this book.

One of my favorite recent mathematics books - and one that offers a nice continuum between 'pure' mathematics and a specific application of it, as well as a nice spread of mathematical sophistication from pop math to some research-level depth, is The Symmetries Of Things by John Conway, Heidi Burgiel and Chaim Goodman-Strauss. It's an exploration of 'discrete' symmetries of the plane and of space - and of the tilings, polyhedra, etc. that they give rise to - as well as an introduction to some aspects of Coxeter groups and a (slightly out-of-place) chapter on the number of finite groups of various orders. I can highly recommend all of Conway's writing, but this is perhaps the finest instance available right now.

there is a really good book on the subject http://www.amazon.com/The-Symmetries-Things-John-Conway/dp/1568812205

Interesting, I have not heard it called that, and don't seem to be able to find other references. I do know that Conway calls the structure Hexasticks (or hexastakes if the pencils are sharpened, which changes the symmetry group). It is discussed for example in The Symmetry of Things. My understanding is that the design comes from George Hart, though I do not think he claims to have invented it.

hey there the bridges conference is about your research topic. Here is a really cute video displaying some of the pieces, which there are descriptions of on the site.

This youtube channel also has a lot of other maths inspired art such as this sculpture and a cute little video on symmetry in music.

Good luck with your project!

e: also thirding the mc escher suggestion :)

e2: also if you're interested here is an accessible book (pdf)on symmetry in mathematics, which as you can imagine, ends up being a relevant topic for thinking about art.

For visual beauty, it's hard to beat The Symmetries of Things (2008) by Conway, Burgiel & Goodman-Strauss.

The MAA review says, "The first thing one notices when one picks up a copy of The Symmetries of Things is that it is a beautiful book."