In each crystallographic group, the group operation means the combination of two symmetry operations. For example,...

 

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In each crystallographic group, the group operation means the combination of two symmetry operations. For example, A B means to apply the symmetry operation defined by B first and then to apply the symmetry operation defined by A. Explain whether and why (or why not) all the translation operations defined by a 2D square lattice (t = ax, t = a. x and are unit vectors in a Cartesian coordinate system) plus the group operation defined above can form a crystallographic group. t = ay t = ax . In each crystallographic group, the group operation means the combination of two symmetry operations. For example, A B means to apply the symmetry operation defined by B first and then to apply the symmetry operation defined by A. Explain whether and why (or why not) all the translation operations defined by a 2D square lattice (t = ax, t = a. x and are unit vectors in a Cartesian coordinate system) plus the group operation defined above can form a crystallographic group. t = ay t = ax .