Vostok Ice Mountain

It is never warm at the Russian antarctic research facility Vostok station. So, ice, and perhaps the solution-looking-for-a-problem that is Pykrete, are cheap and useful building materials. What are we going to build? A massive great mountain. To do this, we're going to need a couple of power stations, nuclear for preference. One at the shore as a pumping station, and another at the site as a second pumping station and general power station. Then, we're going to start pumping water. A team of robots dragging big hoses around take care of spraying water about in a nice square. I'm thinking a square, of about 100km per side. Then, build another, until you have a 40km-tall stepped pyramid. Obviously, nature has stacked miles of ice upon miles of ice and things tend to (very slowly) get away from you in a glacial flux kind of way. To address nature's foolishness, we will incorporate strategic structural ties of Pykrete to stabilize the whole thing against flowing away.

The height is capped at 40km because the atmosphere starts to warm up at high altitude and get's a little close to 0 (unless it's much colder over the antarctic). Again, perhaps a Pykrete cap would be stable at higher altitudes.

Why build it? Why not? You could probably get some pretty atmosphere free images with a nice telescope, although you're not going to cover much sky with a polar location. The location is all wrong for an aurora observatory. You could use it as a support for a space launch track, but again, not the ideal location, the equator would be better there. Mountain climbers would like it. You would need supplementary oxygen of course. And Supplementary nitrogen, supplementary pressure, supplementary most things really since the pressure is only 0.2% of sea level. Still, you might feel sprightly after losing almost 3% of your weight due to gravity changes.