Can someone explain these Definitions about Cell Complexes for me?

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I've been reading "On a small cancellation theorem of Gromov" by Yann Ollivier (https://projecteuclid.org/journalArticle/Download?urlId=10.36045%2Fbbms%2F1148059334 ) recently and these definitions aren't really clear for me since the author never really described what he meant by combinatorial 2-complex. I am also not really sure what he means when talking about faces and multiplicity of faces. Maybe someone has already read this article and give me a hint about what is meant or even draw a picture for me. Thanks!

Definition 4

Definition 5