ax^6 + by^6 + cz^6 = w^2

General case: Parametric solutions are shown.
Individual case: Numerical solutions for fixed (a,b,c).

General case:

     ax^6 + by^6 + cz^6 = w^2 Ⅰ
     
     ax^6 + by^6 + cz^6 = w^2 Ⅱ and ax^6 + by^6 + cz^6 = w^3
     
     ax^6 + by^6 + cz^6 = w^2 Ⅲ
     
     ax^6 + by^6 + cz^6 = w^2 Ⅳ

     ax^6 + by^6 + cz^6 = w^2 Ⅴ
     
     ax^6 + by^6 + cz^6 = w^2 Ⅵ
     
     
Individual case:
           48x^6 + 24y^6 - 72z^6 = w^2 

           48x^6 + 12y^6 - 60z^6 = w^2 

           46x^6 + 12y^6 - 58z^6 = w^2 

           45x^6 + 20y^6 - 65z^6 = w^2 

           42x^6 + 28y^6 - 70z^6 = w^2 

           40x^6 + 24y^6 - 64z^6 = w^2 

           40x^6 + 8y^6 - 48z^6  = w^2 

           39x^6 + 36y^6 - 75z^6 = w^2 

           39x^6 + 13y^6 - 52z^6 = w^2 

           38x^6 + 20y^6 - 58z^6 = w^2 

           38x^6 + 10y^6 - 48z^6 = w^2 

           36x^6 + 12y^6 - 48z^6 = w^2 

           33x^6 + 3y^6 - 36z^6  = w^2 

           30x^6 + 20y^6 - 50z^6 = w^2  

           30x^6 + 6y^6 - 36z^6  = w^2  
           
           28x^6 + 14y^6 - 42z^6 = w^2  

           27x^6 + 12y^6 - 39z^6 = w^2  

           25x^6 + 20y^6 - 45z^6 = w^2  

           24x^6 + 16y^6 - 40z^6 = w^2  

           21x^6 + 7y^6 - 28z^6  = w^2  

           20x^6 + 10y^6 - 30z^6 = w^2  

           20x^6 + 5y^6 - 25z^6  = w^2  

           16x^6 + 9y^6 - 25z^6  = w^2  

           16x^6 + 2y^6 - 18z^6  = w^2  

           15x^6 + 5y^6 - 20z^6  = w^2  

           12x^6 + 6y^6 - 18z^6  = w^2  

           12x^6 + 3y^6 - 15z^6  = w^2  

           10x^6 + 6y^6 - 16z^6  = w^2  

           10x^6 + 2y^6 - 12z^6  = w^2  

           9x^6 + 3y^6 - 12z^6   = w^2  

           6x^6 + 4y^6 - 10z^6 = w^2  

           -27x^6 - y^6 + z^6 = w^2  

           -12x^6 + 6y^6 - 48z^6 = w^2  

           -48x^6 + 6y^6 - 6z^6 = w^2  

           -12x^6 + 6y^6 - 6z^6 = w^2