Hesse configuration

<p>In geometry, the Hesse configuration is a <a href="/facts/Configuration_(geometry)/2EJN52Ud">configuration</a> of 9 points and 12 lines with three points per line and four lines through each point. It can be denoted as (94 123) or configuration matrix 
  
    
      
        
          [
          
            
              
                
                  
                    9
                  
                  
                    4
                  
                
                
                  
                    3
                  
                  
                    12
                  
                
              
            
          
          ]
        
      
    
    {\displaystyle \left[{\begin{smallmatrix}9&4\\3&12\\\end{smallmatrix}}\right]}
  
. It is symmetric (point and line transitive) with 432 <a href="/facts/Automorphism/WnyxNFkQ">automorphisms</a>.
</p><p>It can be realized in the <a href="/facts/Complex_projective_plane/5WFpDyeV">complex projective plane</a> as the set of <a href="/facts/Inflection_point/Ev2dv4WS">inflection points</a> of an <a href="/facts/Elliptic_curve/60jvaHSA">elliptic curve</a>, but it has no realization in the <a href="/facts/Euclidean_plane/tAUtRFcn">Euclidean plane</a>. It was introduced by <a href="/facts/Colin_Maclaurin/nVexkojA">Colin Maclaurin</a> and studied by <a href="/facts/Otto_Hesse/towSdWW9">Hesse</a> (1844), and is also known as Young's geometry, named after the later work of <a href="/facts/John_Wesley_Young/DM3NWAhV">John Wesley Young</a> on finite geometry.
</p>

Hesse configuration open-in-new

Hesse configuration