My terminology for a Non-Normal Magic Hexagon, ie...
to paraphrase the definition found at the MathWorld Resource cited at the bottom of this page,
A Magical Hexagon is an arrangement of n close-packed hexagons containing the numbers k, k+1, k+2, ..., k+(n-1)
where k does not have to equal 1, such that the numbers along each straight line add up to the same magical number.
The Major difference between a Magical Hexagon vrs a Magic Hexagon is slight, where a Magic Hexagon MUST
start with the Low Boudary of 1, while a Magical Hexagon can start with a low boudary not equal to 1.
Now, some might believe that no magic Hexagon can start with a number other than 1, that there is only 1 magic hexagon.
There is a proof, generated by a gentleman By the name of C. W. Trigg, which does indeed prove there is Only 1 Magic Hexagon of a non-trivial
size that starts with the number 1. So, strictly by the definition of a Magic Hexagon, since it requires to start with One, this
has, IMHO, deterred people from investigating non-normal Magic Hexagons.
Non-Normal Magical Hexagons exist, and are distinct from the sole Magic Hexagon widely known.
Unlike Magic Squares, where a NonNormal Magic Square is Additatevely Equivalent to another, Normal, Magic Square,
and therefore is trivial, Non Normal Magical Hexagons cannot be transformed via a simple additive matrix, ie...
you cannot add or subtract a constant number from each cell and end up with another magical hexagon.
There are millions of Magical Hexagons, and the process of developing them is fascinating.