Consider the $n$-cube graph with vertices $\{-1,1\}^n$ and edges connecting vertices with hamming distance $1$. How many hyperplanes in $\mathbb{R}^n$ are needed in order to dissect all edges? We show that at least $\widetildeΩ(n^{2/3})$ are needed, which improves the previous bound of $Ω(n^{0.51})$ by Yehuda and Yehudayoff.