For paracompact hyperbolic honeycombs, there are three groups in dimensions 6 and 9, or equivalently of ranks 7 and 10, with no other forms in higher dimensions.
In dimensions 
  
    
      
        n
      
    
    {\displaystyle n}
   ⩾ 9, the only three uniform polytope families, aside from the numerous infinite proprismatic families, are the 
  
    
      
        
          
            A
          
          
            n
          
        
      
    
    {\displaystyle \mathrm {A} _{n}}
   simplex, 
  
    
      
        
          
            B
          
          
            n
          
        
      
    
    {\displaystyle \mathrm {B} _{n}}
   cubic, and 
  
    
      
        
          
            D
          
          
            n
          
        
      
    
    {\displaystyle \mathrm {D} _{n}}
   demihypercubic families.