In 2021, I. Limonchenko, T. Panov, J. Song and D. Stanley introduced the notion of double (co)homology of a moment angle complex $\mathcal{Z}_K$ associated to a simplicial complex $K$. If $K$ is a triangulated $n$-sphere, the double cohomology of its complex behaves in a particularly interesting manner. In this talk I'll start by summarizing the double homology construction, after that I'll present three results we've put together over the last year. The first one is a computation for a large class of simplicial complexes, the second one is about the case where the complex is a sphere, and lastly, we present a connection between the neighborly property of a complex and their double homology.