In graph theory, what's the difference of triangles and 3-faces?

Question

I'm pretty sure that triangles and 3-faces are not the same but I cannot find their differences according to their definitions. Could you please help me with that?

Thanks

Answer 1

In a planar graph the two notions are equivalent, but the notion of a triangle is more general: a $3$-clique (i.e., a copy of $K_3$) in any graph is a triangle, but the notion of face applies only to planar graphs.