NavList:

Geoffrey Kolbe you wrote: The problem in taking an altitude of Polaris while standing at the North pole is - what direction do you face? Normally, an object is low enough (in altitude) that there is no problem, you stand facing the object. But when the altitude approached 90° then this becomes a significant problem, wherever you are on the planet, and can lead to significant errors. Of course, whichever way you face at the North Pole, you are facing South, which somewhat adds to the problem.

You are correct of course Geoffrey.  If you were certain you were at the pole you could argue that you would measure a sinusoid between 89°20' and 90°40' depending upon which way you were facing. But you could measure similar values in various places out to 80nm from the pole, so the whole thing is ambiguous, even for a zenith fix.  DaveP
AL1. To my 23Jul 13.48.  For variation read declination.