Hatcher 2.1.6

Compute the simplicial homology groups of the $\Delta$ -complex obtained from $n+1$ 2-simplices $\Delta_0^2, \dots, \Delta_n^2$ by identifying all three edges of $\Delta_0^2$ to a single edge, and for $i>0$ identifying the edges $[v_0,v_1]$ and $[v_1,v_2]$ of $\Delta_i^2$ to a single edge and the edge $[v_0,v_2]$ to the edge $[v_0,v_1]$ of $\Delta_{i-1}^2$ .