The first Bike Friday in Europe, imported in 1992 by Hans Voss of Spezialrad GMBH in Itzehoe, Germany. An "idea" bike, with the idea being that a "full-grown" upright posture double-20in wheel bike be made to fit into the largest airline- compliant standard suitcase to permit easy transport of it when traveling. In addition to that the suitcase- container then turns into a trailer, which can be hitched to the bike. Thus one has the option of towing it behind, rather than having to store it somewhere at the starting point of the ride, and ultimately needing to come back to reclaim it.
    This effectively allows one to travel with a soft backpack and the bike in the suitcase, and, at the destination airport, put the backpack into the suitcase- trailer, hitch it up, saddle up and start burning up these calories!
    It must be stated, however, that because of severe space constraints the folding down process is somewhat complex, requiring on the average about half an hour to fit all parts into that constrained hardshell space. Ergo, it is not well suited for commuting- type quick- folding down and carrying up the stairs etc on a permanent basis. For one, the folded bike does not interlock to become an easy to manage object, as does the Brompton.
    There are by now several Bike Friday models available, of which this is the basic World Traveller one. And, to make things "worse", there is even now a Bike Two's Day [a foldable tandem, that fits in two suitcases, which turn into a double- decker trailer] ;-)). They are custom- made to size by a company called Green Gear Cycling in the USA. Though not exactly cheap, they have won quite a following among the must-train- everyday/ must-dash- outtastate members of the cycling community.

    It should be noted, that, in response to wishful- thinking inquries from "wannabents", recumbent enthusiasts envious of the well- made folding upright, the company has at various times stated, that they'll make a recumbent add-on, or a conversion kit for their bike once and IF  they get enough orders to make it worth their while. The magic number for that "bootstrapping" effort tends to vary from 30 to 100.
    Personally, I do not believe for a minute, that they'll EVER do it. For one, they allready have an unique product in a niche almost of their own, and the upright- bike market, their target group, is much larger than the recumbent one. For another, adapting the current design for recumbent use would have meant so many changes, that it might not be entirely sane to pursue that course of action (and GGC folks are extremely down-to- Earth 'uns by the looks of it [Earth in Eugene, Oregon]).
    And then I do not think it physically possible to fit a double- 20in- wheel recumbent into a standard, if large, suitcase. Unlike the upright bike's compact saddle and other frame members, the supine model would require addition of a seat --already that of considerable volume-- not to mention the extended BB tube, longer chainline etc. If that'd be possible at all, the container would have to be custom- fitted to the folded bike, not the other way around.
    And that's where the matter effectively  ends. A custom- size (moulded plastic) suitcase would have been very expensive, too expensive in relation to its function. Buying a $1200+ folder and container- trailer combo is one thing; having to pay a projected extra $500 for the suitcase alone would have made the product that much less enticing. So let us kill off that recurring BF-recumbent- add-on meme [=a thought virus] ONCE AND FOR ALL, and admire the Bike Friday for what it is, not for its purely theoretical , assumed potential.