Δ-complex

Summary

A $\Delta$-complex is a space built by gluing simplices along their faces. Each face of a simplex is identified with another simplex by the order-preserving linear map. It is more flexible than a simplicial complex. A simplex may have several of its faces glued together, and two simplices may share all their vertices. $\Delta$-complexes are the geometric realizations of semi-simplicial sets, also called $\Delta$-sets, and they are the setting of simplicial homology in Hatcher's textbook.