Facepenis is a term used to describe everything wrong with the Cornell University school of engineering. Depending on context it can be synonymous with clusterfuck, but can also be used as an expletive. In conversation it is usually shortened to simply "face."

when you're hungover as shit after a spending a night drunk as a skunk

when someone is wearing a face mask incorrectly, covering their mouth but showing their nose. the term is comparing it to wearing pants with your penis sticking out.

Someone who wears their mask but still exposes their nose