In fact, there are two, in the bathroom on the lower level.

Today I had a chance encounter in the elevator with a woman who was carrying clothes and had wet hair. Since it looked like she had just showered I asked her if there are showers in the building. As it turns out she hadn't used them but pointed me in the right direction. They are a little bit nasty: they have many dead flies on the floor, apparently from lack of use. A quick spray down before use should take care of that! Now, I just need to figure out how to deal with my left turn issue and figure out where to lockup the bike.