In dimensions 
  
    
      
        n
      
    
    {\displaystyle n}
   ⩾ 5, there are only three regular polytopes: the 
  
    
      
        n
      
    
    {\displaystyle n}
  -simplexes, 
  
    
      
        n
      
    
    {\displaystyle n}
  -cubes, and 
  
    
      
        n
      
    
    {\displaystyle n}
  -orthoplexes.
This is because in both the hip and shoulder joints the metaphysis is intra-articular which in turn facilitates the spread of hematogenous osteomyelitis into the joint cavity. Conversely, joint sepsis may spread to the metaphysis and induce osteomyelitis. Acute exacerbation of juvenile idiopathic arthritis and transient synovitis of the hip both of which are non-septic conditions may mimic septic arthritis. More serious and life-threatening disorders as bone malignancies e.g. Ewing sarcoma and osteosarcoma may mimic septic arthritis associated with concurrent acute hematogenous osteomyelitis. In this regard, Magnetic resonance imaging may play an important role in the differential diagnosis. Joint aspiration
In children, joint synovial fluid aspiration techniques aim at isolating the infectious organism by culture and sensitivity analysis. Cytological analysis of the joint aspirate can point to septic arthritis. However, a negative culture and sensitivity test does not rule out the presence of septic arthritis. Various clinical scenarios and technique-related factors may impact the validity of results of the culture and sensitivity. Additionally, results of cytological analysis, though important, should not be interpreted in isolation of the clinical settings. In the joint fluid, the typical white blood cell count in septic arthritis is over 50,000-100,000 cells per 10−6/l (50,000-100,000 cell/mm3); where more than 90% are neutrophils is suggestive of septic arthritis. For those with prosthetic joints, white cell count more than 1,100 per mm3 with neutrophil count greater than 64% is suggestive of septic arthritis. However, septic synovial fluid can have white blood cell counts as low as a few thousand in the early stages.