text: (4/3)S2  (S3  S4) +  2/3(2S1  S2 + 1/2) 
  p 
  −  ·  ×  · 
  (4/3)S3  (S4  S2) +  2/3(2S1  S3 + 1/2) 
  p 
  −  ·  ×  · 
  
  p 
  −  ·  ×  · 
  (10) 
  
  So the symmetry mentioned above can be realized by a 
  three-fold rotation of the honeycomb lattice, with a cyclic 
  permutation of S2, S3 and S4 in each cluster. This is in 
  fact the three-fold rotation symmetry of the physical spin 
  lattice illustrated in FIG. 2. However this more symmet- 
  ric representation will not be used in later part of this 
  paper. 