For my best friend's birthday, I am looking for a geometry book. He's currently doing his math PhD and is really fond of geometry, especially hyperbolic or higher-dimensional ones, also interested in (star or not) polytopes. He is no beginner at all, having read Coxeter or Gromov, so I am looking for a real hard-math book for him.

I looked at Thurston, but it seems most of his works are actually freely available online, and I would prefer not to give him a free-printed pdf as a present :/

It may be a theorem or theory-presentation book, maybe with a historical part though not necessary nor prioritary.

What would you advice to me ?

allof geometry?? That is going to be taugh... $\endgroup$ – Qfwfq Sep 7 '18 at 9:45