There are also a total of five Coxeter groups that generate non-prismatic Euclidian honeycombs in 4-space, alongside five compact hyperbolic Coxeter groups that generate five regular compact hyperbolic honeycombs with finite facets, as with the order-5 5-cell honeycomb and the order-5 120-cell honeycomb, both of which have five cells around each face. Compact hyperbolic honeycombs only exist through the fourth dimension, or rank 5, with paracompact hyperbolic solutions existing through rank 10.
Likewise, analogues of three-dimensional icosahedral symmetry 
  
    
      
        
          
            I
          
          
            h
          
        
      
    
    {\displaystyle \mathrm {I} _{h}}
   or  four-dimensional 
  
    
      
        
          
            H
          
          
            4
          
        
      
    
    {\displaystyle \mathrm {H} _{4}}
   symmetry do not exist in dimensions n ⩾ 5; however, there is the uniform prismatic group 
  
    
      
        
          
            H
          
          
            4
          
        
      
    
    {\displaystyle \mathrm {H} _{4}}
   × 
  
    
      
        
          
            A
          
          
            1
          
        
      
    
    {\displaystyle \mathrm {A} _{1}}
   in the fifth dimension which contains prisms of regular and uniform 4-polytopes that have 
  
    
      
        
          
            H
          
          
            4
          
        
      
    
    {\displaystyle \mathrm {H} _{4}}
   symmetry.