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Nice observation, Jonathan. Maybe it's the Americanized version of the GR4G ;-) http://www.tube-tester.com/sites/nixie/data/gr4g/gr4g.htm
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I suppose there are two reasons why so many pins are present. One is locating the right position of the tube - if you skip most of the pins, then orientation can be located only by judging where the front of the tube is. If there is only one way to put something in something, then the risk of something wrong happening is minimized.
Also, if the socket has all 27 slots present, but the tube doesn't, someone might thing his tube is broken, as it has less pins.
The other reason is that as far as I know the stems weren't produced by the same companies, or at least not in same factories, so ordering unique bases was more problematic than just purchasing same type as for the other tubes.
Actually, in most if not all of the voltage regulator/voltage reference tubes, at least a pair of the pins are used as security feature. This is just a short circuit between two pins that are used to disconnect the output of the power supply when the regulator is not in the socket to avoid unregulated high voltage going into the load when the regulator/reference is not in.
It is interesting to see that very few of the new circuits that use this voltage regulators do not make use of this security feature.