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Across income groups and countries, individual citizens perceive economic inequality spectacularly wrong. These misperceptions have far-reaching consequences, as it is perceived inequality, not actualinequality informing redistributive preferences. The prevalence of this phenomenon is independent of social class and welfare regime, which suggests the existence of a common mechanism behind public perceptions. The literature has identified several stylised facts on how individual perceptions respond to actual inequality and how these biases vary systematically along the income distribution. We propose a network-based explanation of perceived inequality building on recent advances in random geometric graph theory. The generating mechanism can replicate all of forementioned stylised facts simultaneously. It also produces social networks that exhibit salient features of real-world networks; namely, they cannot be statistically distinguished from small-world networks, testifying to the robustness of our approach. Our results, therefore, suggest that homophilic segregation is a promising candidate to explain inequality perceptions with strong implications for theories of consumption and voting behaviour.