> For a 3D object like a glass A glass is not convex so this theorem does not apply. You'd need other fixed-point theorems for that. If the glass has a handl

> For a 3D object like a glass A glass is not convex so this theorem does not apply. You'd need other fixed-point theorems for that. If the glass has a handle the result is trivially false (consider rotating a doughnut, this does not have any fixed point).