Prisms

prisms.py

In [112]: def find_prisms(): 
     ...:     found = set() 
     ...:     for a in range(1,10000): 
     ...:         for b in range(1,10000): 
     ...:             numerator = 2*a*b 
     ...:             denominator = a*b - 2*a - 2*b 
     ...:             if denominator > 0: 
     ...:                 c = numerator/denominator             
     ...:                 if c.is_integer(): 
     ...:                     found.add(tuple(sorted((a,b,int(c))))) 
     ...:     return found 
     ...:  
     ...:      
     ...:                  
     ...:              
     ...:                                                                                                                     

In [113]: a = find_prisms()                                                                                                   

In [114]: print(a)                                                                                                            
{(3, 8, 24), (3, 9, 18), (4, 8, 8), (4, 6, 12), (6, 6, 6), (3, 12, 12), (3, 10, 15), (3, 7, 42), (4, 5, 20), (5, 5, 10)}