There are exclusively twelve complex aperiotopes in 
  
    
      
        
          
            C
          
          
            n
          
        
      
    
    {\displaystyle \mathbb {C} ^{n}}
   complex spaces of dimensions 
  
    
      
        n
      
    
    {\displaystyle n}
   ⩾ 
  
    
      
        5
      
    
    {\displaystyle 5}
  , with fifteen in 
  
    
      
        
          
            C
          
          
            4
          
        
      
    
    {\displaystyle \mathbb {C} ^{4}}
   and sixteen in 
  
    
      
        
          
            C
          
          
            3
          
        
      
    
    {\displaystyle \mathbb {C} ^{3}}
  ; alongside complex polytopes in 
  
    
      
        
          
            C
          
          
            5
          
        
      
    
    {\displaystyle \mathbb {C} ^{5}}
   and higher under simplex, hypercubic and orthoplex groups, the latter with van Oss polytopes.
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.