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I don't have the subject knowledge to comment on the regulator, but I've been obsessing all afternoon about the identity of the mask without coming to a definitive conclusion. I just wish I had one of those computer programs on CSI that could turn a fuzzy low-resolution image of a vehicle number plate into a crystal-clear high-resolution picture revealing the whole string of letters and numbers, because then I would be able to decypher the manufacturer's marks on the mask lens and solve the identification problem.
Rectangular diving masks were much rarer than oval masks during the vintage era, but they were known to provide a wider field of vision than oval masks, which is why Cousteau at one time equipped his divers with La Spirotechnique Aquarama masks to highlight their eyes on underwater films:
One French manufacturer, Edouard Godel, successor to Louis de Corlieu, the original modern inventor of swimming fins, specialised in rectangular diving masks with rounded corners like the one worn by the small girl: Godel Cyclope
However, the precise shape of the Godel masks isn't quite right. I'm trying to figure out whether this might be a "junior" underwater mask designed for the children's market and therefore an entry-level model without refinements such as a lens-retaining stainless-steel band with a top screw. Children's masks are often consigned to a different section of a diving equipment manufacturer's catalogue where they can be overlooked. I'll keep trying to find a plausible candidate for that mask.