650B is the french designation for a wheel that is 584mm in diameter according to the ETRTO standard, placing it between 559mm (26") usual MTB size and 622mm (28") the ubiquitous road bike size. In Germany sizes like these are dubbed in-between sizes as if to say they're neither here nor there.
650B however is enjoying a renaissance partly due to the work of Kirk Pacenti in designing a tyre in this size for MTBs called the neo-moto.
A smaller but growing following of the 650B size sees its qualities in building compact fast touring bikes or city bikes with wider than usual tyres (28-40mm). As Sheldon Brown pointed out, a wheel with a wide 650B tyre is roughly equivalent in diameter to a 28" with a skinny tyre so there's little difference in gear ratio or momentum. The benefit is the commfort that comes with the wider tyre cycled at a lower pressure.
So what does a 650B Mixte look like? Well I'm going for the classical design with the twin lateral tubes running from the rear dropouts right up to the head-tube. Yo

It might seem like putting the cart before the horse but I wanted to be sure I had a set of wheels before I built a 650B dedicated bike. Having the wheels at hand while your building is handy for checking alignments, brake boss position, mudguard clearance and so on.
Rims in this size are hard to come by in Germany. The only ones I found being old Mavic 40-hole alloy rims from Bruegelmann for 12€ each. I bought a pair not realising just how hard it would to find a set of 40-hole hubs. I eventually tracked down the necessary hubs to build the nicest wheelset I've built yet. So I thought I'd share a few pictures. The front hub is hi-flange Sansin and on the back it's a Campagnolo Record for a free-hub.