In a standard magic star, or magic polygram, numbers are placed at each vertex and intersection to produce lines of four that each sum to the same magic total. This is one possible arrangement for the magic hexagram, for example, using the numbers 1-12 and the magic total 26:

             6              
            . .             
           .   .            
          .     .           
          .     .           
5........7......11........3 
 .      .         .      .  
  .    .           .    .   
   .  .             .  .    
   . .   Hexagram    . .    
    9                 1     
   . .  Magic = 26   . .    
   .  .             .  .    
  .    .           .    .   
 .      .         .      .  
4........2.......12.......8 
          .     .           
          .     .           
           .   .            
            . .             
             10
This is a possible arrangement for the magic heptagram, using the numbers 1-14 and the magic total 30:

                               
        9.           .4        
        . ...     ... .         
       .     .. .     .        
       .   ....8...    .        
       ....        .....        
     ..13              2..      
  ... .                 . ...   
5.    .                 .    .11
 .   .     Heptagram     .   .  
  .. .                   . ..   
    7     Magic = 30     10     
    ..                   ..     
    . .                 . .     
    .  ..             ..  .     
   .     .           .     .    
  1......12.........3.......14  
           .       .            
            ..   ..             
              . .               
               6
And this is a possible arrangement for the magic octagram, using the numbers 1-16 and the magic total 34:

               6                
             .. ..              
            .     .             
    4.....13.......16.....1     
    .    .           .    .     
    .  ..             ..  .     
    . .                 . .     
    12                   10     
   ..                     ..    
 .. .      Octagram       . ..  
3   .                     .   .2 
 .. .     Magic = 34       . .  
   ..                     9.    
    11                   ..     
    . .                 . .     
    .  ..             ..  .     
    .    .           .    .     
    7.....5........8.....14     
            .     .             
             .. ..              
               15
External Link

For further examples and discussion of magic stars, please visit the following website:

Harvey Heinz's Magic Stars