Maybe they called it "face" and not "edge" because an edge is normally understood to be what's between two vertices (of a graph; so an edge has two vertices, beginning and end), while here "face" is what's between two corners of a given triangle (so a face can contain more than two vertices, and so multiple edges).
See the bottom "face" of the top centre triangle in the 4 examples.
Yeah, that's exactly it! "Face" is the term used in the original paper, so that's what I was using. I've updated the page to make the distinction clearer. Thanks!
Comments
That should be 'edge', not 'face', no? Otherwise I do not understand what is happening at all with the examples.
Yes, this would more normally be called "edge". It's not incorrect to call it a face, by analogy with higher-dimensional solids, but confusing.
Maybe they called it "face" and not "edge" because an edge is normally understood to be what's between two vertices (of a graph; so an edge has two vertices, beginning and end), while here "face" is what's between two corners of a given triangle (so a face can contain more than two vertices, and so multiple edges).
See the bottom "face" of the top centre triangle in the 4 examples.
Yeah, that's exactly it! "Face" is the term used in the original paper, so that's what I was using. I've updated the page to make the distinction clearer. Thanks!
They're dealing with planar graphs, graphs embedded in planes. Faces are not edges.
https://en.wikipedia.org/wiki/Planar_graph#Euler's_formula
Pretty sure they meant the word face, that would be the generic term for edge. (An edge being a 1 dimensional face)