Example 1.2.4.4. The horns contained in $\Delta ^2$ are depicted in the following diagram:
\[ \xymatrix@R =20pt@C=20pt{ & \{ 1\} \ar@ {-->}[ddr] & & & \{ 1\} \ar [ddr] & & & \{ 1\} \ar [ddr] & \\ & \Lambda ^{2}_{0} & & & \Lambda ^{2}_{1} & & & \Lambda ^{2}_{2} & \\ \{ 0\} \ar [uur] \ar [rr] & & \{ 2\} & \{ 0\} \ar [uur] \ar@ {-->}[rr] & & \{ 2\} & \{ 0\} \ar@ {-->}[uur] \ar [rr] & & \{ 2\} . } \]
Here the dotted arrows indicate edges of $\Delta ^2$ which are not contained in the corresponding horn.