Conjures up images of the 10X55R Sauer, if such a bird existed, but I think the rim was a bit larger. I like Lancaster's blind guess but I couldn't say what the rim diameter might be. If it is the 10X60R Hunting or 400 Express, we may have a match:

Case: 60mm
Rim: 13.95mm
Base: 11.35
but it does have a neck of 10.6mm

Kind Regards,