Does anyone know if anyone still makes concave rims, also, do they provide any benefits?

A little backup information here, my father just turned 50, he has been a cyclist since he was a boy, for the last ~20 years hes ridden a recumbent but has recently been expressing interest in moving back to a road bike, my entire life my fathers told be about a cycle tour he took with his brother through germany. These conversation often turn to how much he loved the bike he rode on this trip (which was unfortunately totaled), the concave rims that his bike sported come up often, I would like to build a road bike for him before he loses intrest in cycling or become to old to ride (he's fairly athletic so I doubt this will be too soon).

Any information would be appreciated, my dads done alot for me and I would really love to be able to build up a bike like the one he talks about so often (the concave rims are a really big part of the build, if only for the nostalgia)
Thanks for any help.