There are also sixty-four (or 64 = 43) four-dimensional Bravais lattices, and sixty-four uniform polychora in the fourth dimension based on the same 
  
    
      
        
          
            A
          
          
            4
          
        
      
    
    {\displaystyle \mathrm {A} _{4}}
  , 
  
    
      
        
          
            B
          
          
            4
          
        
      
    
    {\displaystyle \mathrm {B} _{4}}
  , 
  
    
      
        
          
            F
          
          
            4
          
        
      
    
    {\displaystyle \mathrm {F} _{4}}
   and 
  
    
      
        
          
            H
          
          
            4
          
        
      
    
    {\displaystyle \mathrm {H} _{4}}
   Coxeter groups, and extending to prismatic groups of uniform polyhedra, including one special non-Wythoffian form, the grand antiprism.
In logic and philosophy
The symbolic meanings of the number four are linked to those of the cross and the square. "Almost from prehistoric times, the number four was employed to signify what was solid, what could be touched and felt. Its relationship to the cross (four points) made it an outstanding symbol of wholeness and universality, a symbol which drew all to itself". Where lines of latitude and longitude intersect, they divide the earth into four proportions. Throughout the world kings and chieftains have been called "lord of the four suns" or "lord of the four quarters of the earth", which is understood to refer to the extent of their powers both territorially and in terms of total control of their subjects doings. The Square of Opposition, in both its Aristotelian version and its Boolean version, consists of four forms: A ("All S is R"), I ("Some S is R"), E ("No S is R"), and O ("Some S is not R"). In regard to whether two given propositions can have the same truth value, there are four separate logical possibilities: the propositions are subalterns (possibly both are true, and possibly both are false); subcontraries (both may be true, but not that both are false); contraries (both may be false, but not that both are true); or contradictories (it is not possible that both are true, and it is not possible that both are false). Aristotle held that there are basically four causes in nature: the material, the formal, the efficient, and the final.