Name for map associated with simplicial complex

Question

Given a simplicial complex $\Delta$, implied by the construction process there are associated maps sending euclidean standard simplices into the simplicial complex $\imath: \Delta^n \to \Delta$. What is the name of those maps? Associated maps, canonical maps, characteristic maps,...?

Answer 1

In Hatcher's Algebraic Topology, these are called characteristic maps, and the restriction $\varphi\colon \partial\Delta^n\to \Delta$ to the boundary is referred to as the attaching map. In my experience, this usage is fairly standard.