The correlation between growth twinning and crystalline reorientation of faceted growth materials during directional solidification was demonstrated through matrix calculation and Thompson regular tetrahedron model diagrams. The correlation is that the crystalline reorientation results from the mirror symmetry operation of initial orientation on different twin planes. In total, seven possibilities of crystalline reorientation caused by single-twinning from ⟨110⟩, ⟨111⟩, and ⟨112⟩ initial axial orientation were predicted, four of which were verified experimentally in the representative Tb0.3Dy0.7Fe2 alloys.