Yes, that's what I get too. Thanks very much for checking.

Thanks. So, for example, the orbit of the first representative is {∞012} {∞123} {∞234} ..., and the orbit of the last one is {0179}, {128a}, {2390}, ...? I tried entering this simplicial complex into SageMath to compute the homology, and it doesn't seem to be $\mathbb{Q}$-acyclic.

I'm confused too. How does $\mathbb{Z} / 11 \mathbb{Z}$ act on the set $\{ 0, ...., 10, \infty \}$? Is $\infty$ a fixed point, and everything else shifts according to $\mod 11$ arithmetic?