Definition 13.1.12 (Affinely Independent).label We say $\curl{v_0,...,v_k}\suf\R^{n}$ is affinely independent if $v_{1}-v_{0},...,v_{k}-v_{0}$ are linearly independent. This is independent of the ordering. We call $Conv(\curl{v_0,v_1,...,v_k})$ a $K$-simplex