According to this page Gillette produced a 3 piece ball end tech, a blue tip , red tip and flare tip super speed, the TV special, the toggle and the "fat boy" adjustable.
This page documents what we know about Gillette safety razor serial numbers and date codes. Razors made in USA often left the factory with serial numbers or date codes, which can be used to establish their manufacturing dates. During certain periods so
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The fat handles were only in the first half of the 1950s. The latest I have seen are around 1954.
There might be some fat handles made in Brazil or Argentina after that, but try and find one.
The only one that remained with a fat handle even in the 70s is the Psycho Tech. Very rare.