So this really is an intriguing (and for the moment unique) transistor radio for the collectors out there with plenty of scope for research. In all likelyhood it was a prototype which never made it into mass production.
When Toshiba entered the Transistor radio market in 1957 they did so with gusto producing a score of beautiful, iconic and sometimes bizarre radios. Most of the early Toshiba transistor radio models have now been well documented, but despite endless searches I have yet to find any mention of this particular model anywhere (even in Japanese). Furthermore after contacting the archivist at Toshiba in Japan they are also unable yet to shed any more light on this fascinating little radio. The dial numbers suggest it was intended for the US market probably as a pocket-sized desk top radio, but the plain and unusual shape is also reminiscent of models intended for use on a car dashboard (but this has no mounting points so would slip around if so). Interestingly the three divots on the top suggest it may also have been designed for something to rest on top of it, but again this is all just speculation.
All we do know is that the model number is very unusual and although it is clearly an official Toshiba product, still has some very hand constructed elements (such as the screws that hold the name plate on and the somewhat flimsy battery flap). All of this suggests a working prototype.