a face with a smile to show people that the person is happy for them, but without having true emotions.
In the Big Bang Theory TV series, Sheldon’s koala face is the smile that forms on his face when he’s watching koalas eat eucalyptus at the zoo. He uses the same face to show people (his girlfriend
Amy in specific) that he is happy for them.
Sheldon: Thank you. Amy, I’d like to apologize. Your accomplishment was impressive. And I’m proud of you.
Amy: We both know that’s your koala face.