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Non-layered two-dimensional (2D) materials have sparked much interest recently due to their atomic thickness, large surface area, thickness- and facet-dependent properties. Currently, these materials are mainly grown from wet-chemistry methods but suffer from small size, low quality, and multi-facets, which is a major challenge hindering their facet-dependent property studies and applications. Here, we report the facet-engineered growth (FEG) of non-layered 2D manganese chalcogenides (MnX, X = S, Se, Te) based on the chemical vapor deposition method. The as-grown samples exhibit large-area surfaces of single facet, high-crystallinity, and ordered domain orientation. As a proof-of-concept, we show the facet-dependent electrocatalytic property of non-layered 2D MnSe, proving they are ideal candidates for fundamental research. Furthermore, we elucidate the underlying mechanism of FEG during the vapor growth process by the interfacial energy derived nucleation models. The method developed in this work provides new opportunities for regulating and designing the structure of 2D materials. [ABSTRACT FROM AUTHOR]