k-points of triangular lattice

Hi, mpb users

In the example of bands of the triangular lattice, the k-points are set as

(set! k-points (list (vector3 0 0 0)          ; Gamma
                     (vector3 0 0.5 0)        ; M
                     (vector3 (/ -3) (/ 3) 0) ; K
                     (vector3 0 0 0)))        ; Gamma
(set! k-points (interpolate 4 k-points))

well, I don't understand why the vector of K point is set as (-1/3, 1/3, 
0)  but not (sqrt(3)/6, 0.5, 0)  according to the irreducible Brillouin 
zone of a triangular lattice?

best regards!
Bin Shao