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LaGaO3 single crystals, grown by the method of zone melting without a crucible, with radiation heating, were investigated by X-ray topography and diffractometry. It has been found that at 293 K these crystals have an orthorhombic unit cell with a = 5.520 (2), b = 5.490 (2), c = 7.770 (1) Å and twinning in the {110}/ 〈10〉 and {112}/〈10〉 systems simultaneously. Regions of cross-twinning have been discovered in these systems. A first-order phase transition from orthorhombic to rhombohedral has been observed at 412.5 K, the cell parameters being a = 3.889 Å, α = 89.50° (423 K). The rhombohedral phase has a developed twin structure in the {100}/〈001〉 and {110}/〈001〉 systems. During transformation the structure undergoes an inherited change to the twin structure of the orthorhombic phase.