QJB,
please see here from another PPRUNE thread:
http://www.pprune.org/questions/1078...ver-poles.html
Some routes will actually go very near or over the poles, as FlyingForFun pointed out, and there is further information from the ATPL theory exams.
As one approaches the North Pole,the heading may change very quickly; please see here pp. 3-4:
http://www.freelancepilot.nl/ATPL%20summary.pdf
There also needs to be a fuel-freeze strategy and monitoring for North Pole operations.
Pay special attention to Glueball's post from the thread I linked to you, but please read all posts.
He really thoroughly offers a full treatment to the question at hand.
I give credit to all those posters from Flying over the poles started Nov 2003 for providing far better explanations than I.
Please see here:
Emirates A330 Flies Over The North Pole! — Civil Aviation Forum | Airliners.net Interesting related flight occurrence over the NP.