From the article "f-vectors of acyclic complexes" (Discrete Math. 1985) by Gil Kalai, we know that the relation between f-vectors of an acyclic simplicial complex. In other words, one can construct an acyclic simplicial complex using Kalai's formula. I tried but didn't manage to construct one.
Can anyone please give me an example of a connected non-contractible acyclic finite simplicial complex?
Thanks in advance. Any help will be appreciated.