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Clustering–the tendency for neighbors of nodes to be connected–quantifies the coupling of a complex network to its latent metric space. In random geometric graphs, clustering undergoes a continuous phase transition, separating a phase with finite clustering from a regime where clustering vanishes in the thermodynamic limit. We prove this geometric-to-nongeometric phase transition to be topological in nature, with anomalous features such as diverging entropy as well as atypical finite size scaling behavior of clustering. Moreover, we see that the dimension of the sufficient statistic of the system diverges at the critical point. Finally, a slow decay of clustering in the nongeometric phase implies that some real networks with relatively high levels of clustering may be better described in this regime