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We present a new, explicit and very geometric construction for the iteratedclique graphs of the hexagonal lattice $\mathrm{Hex}$ which makes apparent itsclique-divergence and sheds light on some previous observations, such as theboundedness of the degrees and clique sizes of $k^n \mathrm{Hex}$ as$n\to\infty$.

The clique graphs of the hexagonal lattice -- an explicit construction and a short proof of divergence