Why does the commander wear a mask in the command center?
It's been a while since this was asked and is pretty much covered in the comments, but here's an answer.

Captain Kobayashi is part of the immortal council and therefore doesn't age. If she walked around never aging people would notice, hence the mask. It probably also serves as a way to hide emotion from the crew, show strength and all that.

Sidonia's wikia page is pretty barren, but there is some stuff there.