The 12SK7 is a variable μ pentode for RF and IF amplifiers in superhet receivers. The gain of the device being controlled by a negative voltage derived from rectifying the final IF signal. In this way strong signals do not overload the receive chain because the various controlled stages have their gain reduced.
The 12.6 Volt heater was introduced so that the heater could be run directly from a vehicle battery. It would have been common to find these valves in professional mobile equipment. For fixed station use the 6SK7 was an identical device in all other respects.
The outer screen.
The IO base pins.
Thanks to Mark Mallison for sending the images.
The wide glass tube envelope is mm in diameter and, excluding the IO base pins, is mm tall.
References: Datasheet, 4055, 3002 & 1040. Type 12SK7GT was first introduced in 1940.