Vintage longines, definition of reference. Unusual case, never seen anything like it before. Probably a very rare model. Movement 2517.

 

That is a really cool-looking case, which I have not seen before. Do you have photos of the movement and inside of the case-back?

 

Looked at a lot of directories? But never came across such a case.

 

Thanks for these additional photos.

Seems to be from circa 1936. I imagine that Longines could tell you the reference number if you are interested.