Solids are generally classified into three categories based on their atomic arrangement: crystalline, quasicrystalline and amorphous1-4. Here we report MgO and Nd2O3 ceramic phases with special atomic arrangements that should belong to a category of solids different from these three well known categories by combining state-of-the-art atomic-resolution scanning transmission electron microscopy and first-principles calculations. The reported solid structure exhibits a one-dimensional (1D) long-range order with a translational periodicity and is composed of structural units that individually have atomic arrangements similar to those observed in coincidence-site lattice configurations present at grain boundaries. Regardless of the insulating nature of the bulk MgO, the bandgap of which is measured to be 7.4 eV, the MgO 1D ordered structure is a wide-bandgap semiconductor with a bandgap of 3.2 eV owing to this special atomic arrangement. The discovery of 1D ordered structures suggests that the structural categories of solids could be more abundant, with physical properties distinct from their regular counterparts.