
There are 50 classes of Pantactic Squares, and within each class there are 16 different forms of the Square that differ from one another by rotations, reflections and color inversions.
I have taken one of these 50 classes  the one I designate Class 9a  and applied all 16 combinations of these transformations to show you the 16 squares that belong to this one class.
To create the 16 members of Class 9a, I either applied or didn't apply the following four actions, in this order, to the original square:
1000  Inversion  changing every black square to white, and viceversa
0100  Leftright reflection
0010  Topbottom reflection
0001  Reflection about the diagonal axis that goes from upperleft to lowerright
There are 16 ways to apply or not apply each of these transformations individually. I numbered the 16 ways by adding up the code numbers listed for each of the transformations. You will see this sum, printed as a caption under each of the Squares, below.
The one labeled "0000" is the original square, the representative of Class 9a. The one labeled 0110, for example, is the one that has had the 0100 (leftright reflection) and 0010 (topbottom reflection) done to it, in that order.
9a 0000 
9a 0001 
9a 0010 
9a 0011 
9a 0100 
9a 0101 
9a 0110 
9a 0111 
9a 1000 
9a 1001 
9a 1010 
9a 1011 
9a 1100 
9a 1101 
9a 1110 
9a 1111 
Every rotation and reflection of the 9a class representative is included here, even though no rotation was explictly performed. For example, to perform a 90ยบ counterclockwise rotation, all you need to do is a leftright reflection followed by a diagonal reflection (9a 0101, above). You will see that 9a 0011 and 9a 0110 are other rotations of the original Square.
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The webmaster and author of this Math Help site is Graeme McRae.