Interesting. Ice is likely to persist at the poles if there's something to attach to (even if there's not if it's cold enough). Antarctica has an ice cap about 2 miles thick, despite receiving effectively zero precipitation. Wikipedia suggests that the buildup at the actual pole is due largely to blown-in snow due to high winds.

My interest in the polar regions was mostly due to the continents being almost exactly centered on the poles. If that's land + ice, then it makes sense.

Here's a Wagner VII (equal-area) projection with a couple of stereographic endcaps.
combo.png