Owing to its scientific and technological importance, crystallization as a ubiquitous phenomenon has been widely studied over centuries. Well-developed single crystals are generally enclosed by regular flat facets spontaneously to form polyhedral morphologies because of the well-known self-confinement principle for crystal growth. However, in nature, complex single crystalline calcitic skeleton of biological organisms generally has a curved external surface formed by specific interactions between organic moieties and biocompatible minerals. Here we show a new class of crystal surface of TiO₂, which is enclosed by quasi continuous high-index microfacets and thus has a unique truncated biconic morphology. Such single crystals may open a new direction for crystal growth study since, in principle, crystal growth rates of all facets between two normal {101} and {011} crystal surfaces are almost identical. In other words, the facet with continuous Miller index can exist because of the continuous curvature on the crystal surface.
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