A polyhedral surface~$\mathcal{C}$ in $\mathbb{R}^3$ with convex polygons as faces is a side-contact representation of a graph~$G$ if there is a bijection between the vertices of $G$ and the faces of~$\mathcal{C}$ such that the polygons of adjacent vertices are exactly the polygons sharing an entire common side in~$\mathcal{C}$. We show that $K_{3,8}$ has a side-contact representation but $K_{3,250}$ has not. The latter result implies that the number of edges of a graph with side-contact representation and $n$ vertices is bounded by $O(n^{5/3})$.

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