Is it possible for three simplices to share the same face (for the standard definition of simplical complex)?
In this website (http://www.cs.cmu.edu/afs/cs/project/pscico/pscico/src/simpcomp/README.html), it is written, "A simplicial set is similar to a simplicial complex but more general. A simplicial set allows three or more simplices share the same face.", implying that for regular simplicial complexes this is not allowed.
However, consider the simplicial complex made up of 5 vertices and 4 lines in the shape of an X. Then, surely, the 4 1-simplices share the same face, i.e. the vertex (0 simplex) in the middle?
Thanks for any help.