Complex sentence: John Flinders Petrie was a lifelong friend of Coxeter's with a remarkable ability to visualise four-dimensional geometry, and he and Coxeter had worked together on many mathematical problems.
Split into simpler sentences: John Flinders Petrie was a lifelong friend of Coxeter and had a remarkable ability to visualise four-dimensional geometry. He and Coxeter had worked together on many mathematical problems.