The boundary of Δn\Delta^nΔn is ∂Δn:=⋃i=0n[v0,…,v^i,…,vn]\partial \Delta^n := \bigcup^n_{i=0} [v_0, \dots, \widehat{v}_i, \dots, v_n]∂Δn:=i=0⋃n[v0,…,vi,…,vn] The interior of Δn\Delta^nΔn is Δn∖∂Δn\Delta^n \setminus \partial \Delta^nΔn∖∂Δn.