I've noticed that polar expeditions seem to favour tunnel tents, and mountaineering expeditions prefer geodesic designs. Is there a reason why one design fares better than the other in its preferred environment?
The key advantage of a geodesic design is the pole configuration can support a greater static load. This means they are favoured for mountaineering expeditions because they can withstand a heavy snow fall (compared with a tunnel design that would sag with the weight of the snow between each pole).
Tunnel tents are preferred for polar expeditions as they generally have a better weight to space ratio (the walls are more "vertical" than an equivalent geodesic design), they are simpler and quicker to pitch and as many regions of the Poles have little precipitation (some areas being classified as desert) the ability to withstand heavy snowfall is much less of a consideration.