Let $F_{i,p}: \Delta_{p-1} \rightarrow \Delta_{p}$ denote the $i$-th face map i.e. the map that maps $e_0 \mapsto e_0$,$\dots$,$e_i \mapsto e_{i+1}$,$\dots$,$e_{p-1} \mapsto e_p$.
Let's consider $\Delta_2$ (the triangle) and let its vertices be $e_0, e_1, e_2$.
Now I want to write down $F_{0,2}$:
$F_{0,2}(e_0, e_1) = e_1 e_2$, OK
$F_{0,2}(e_1, e_2) = e_2 (?)$
$F_{0,2} (e_0, e_2)= e_0 (?)$
Can someone tell me what happens in the other two cases? It seems the definition of face map can't cope with those cases. Thanks for your help!