I am really keen on exploring the geometry of polyhedra particularly the representation of their symmetries by groups (not being a mathematician I do not care much for higher dimensional polytopes). I have been recommended Coxeter's book "Regular Polytopes". I went through the contents and guessed that the author concerns himself more about n-dimensional polytopes rather than what I want: 3d polyhedra - so I decided not to buy the book yet and first ask for recommendations here. Does anyone have any recommendations?
My mathematical background: I am pursuing an undergraduate degree in physics so I know trigonometry, calculus, and linear algebra well. I also know what a 'group' means although I haven't studied the theory in detail. Most importantly, I am willing to go through the hard math if required if it leads me to my purpose and if the book is not too 'dry'.
Thank you for your time.
You might enjoy Peter Cromwell's Polyhedra, and you can view its table of contents here.
As you can see, a lot of the book is historical (but to be fair, polyhedra have a long and interesting history). While I certainly haven't read the book cover-to-cover (and thus can't make a very strong recommendation), what I have read has been very nice. Chapters 2, 4, and 8-10 (so roughly half of the chapters) will probably be where most of the discussion of symmetry occurs, so the book is definitely about more than symmetry.