The 5-simplex has the Coxeter group 
  
    
      
        
          
            A
          
          
            5
          
        
      
    
    {\displaystyle \mathrm {A} _{5}}
   as its symmetry group, of order 720 = 6!, whose group structure is represented by the symmetric group 
  
    
      
        
          
            S
          
          
            6
          
        
      
    
    {\displaystyle \mathrm {S} _{6}}
  , the only finite symmetric group which has an outer automorphism.
Factor V (pronounced factor five) is a protein of the coagulation system, rarely referred to as proaccelerin or labile factor. In contrast to most other coagulation factors, it is not enzymatically active but functions as a cofactor. Deficiency leads to predisposition for hemorrhage, while some mutations (most notably factor V Leiden) predispose for thrombosis. Genetics
The gene for factor V is located on the first chromosome (1q24). It is genomically related to the family of multicopper oxidases, and is homologous to coagulation factor VIII. The gene spans 70 kb, consists of 25 exons, and the resulting protein has a relative molecular mass of approximately 330kDa. Structure
Factor V protein consists of six domains: A1-A2-B-A3-C1-C2. The A domains are homologous to the A domains of the copper-binding protein ceruloplasmin, and form a triangular as in that protein. A copper ion is bound in the A1-A3 interface, and A3 interacts with the plasma.The C domains belong to the  phospholipid-binding discoidin domain family (unrelated to C2 domain), and the C2 domain mediates membrane binding. The B domain C-terminus acts as a cofactor for the anticoagulant protein C activation by protein S.Activation of factor V to factor Va is done by cleavage and release of the B domain, after which the protein no longer assists in activating protein C. The protein is now divided to a heavy chain, consisting of the A1-A2 domains, and a light chain, consisting of the A3-C1-C2 domains. Both form non-covalently a complex in a calcium-dependent manner.