Vintage longines, definition of reference

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