Jeff and I worked on the problem for several years. Once he visited me with his family for two weeks. Before the visit I emailed him and asked: What should we work on in your visit?
Jeff asnwered: We should settle Borsuk’s problem!
I asked: What should we do in the second week?!
and Jeff asnwered: We should write the paper!
And so it was.
You can download our paper here. Here is the proof itself.