This is a (3 x 3)R30 structure
The rotated unit cell is illustrated below - note, the hexagonal symmetry of the substrate is also evident in the overlayer structure.
The vectors b1 and b2 are longer than a1 and a2 by a factor of 3.
This is easily proved by noting
The length of the b vectors may therefore be obtained by considering an isosceles triangle with an angle of 120 degrees between the two sides which are of identical length (a), and applying the cosine rule to find the length of the third side (b).
b2 = a2 + a2 - 2.a.a cos 120 = 3 a2 ⇒ b = 3 a
The angle between the b2 and a2 vectors (and between the b1 and a1 vectors is 30 degrees)
Hence, this is a (3 x 3)R30 structure.
What is the matrix description for this structure ?