Triangulation (plane graphs) - graph vs multigraph

Question

I have the following (general) definition of triangulation.

Definition: A triangulation is a plane multigraph G (on ≥ 3 vertices) such that each face of G (including the outer face) is bounded by a triangle of G.

Hovewer, there is this note I do not undarstand.

Note that a triangulation need not be a simple graph (possible parallel edges do not bound a common face).

I think it means there exists a plane multigraph that matches the definition, but is not isomorphic to any simple plane graph, like this one.

However, what does "possible parallel edges do not bound a common face" mean? Does "bound" mean "merge/join", or "separate/cut in two"? Dictionary says "bound" is from "bind", meaning "to merge/get together", but frome the picture it looks more like "to separate the same face in two".

Note: I assume "simple graph" = "not a multigraph" = "for each two vertices there is only one edge that connects them"

Answer 1

In this context, "bound" means "form the boundary of." As seen in your example, parallel edges are each part of the boundaries of triangular faces, but they are not part of the boundary of the same face.