Cubic as well as hexagonal single crystals of C₇₀ have been grown and investigated by electron diffraction, electron microscopy and x-ray diffraction. Several phase transitions have been detected and crystallographic models are proposed. Hexagonal crystals, stable at room temperature with c/a = 1.63 will undergo two transitions, upon cooling. First the c/a ratio will increase to 1.82 owing to c-axis alignment of the molecules; at a lower temperature the molecules will orientationally order, resulting in a monoclinic structure.