Log24

In the mind of the mathematician,
Among the figures and forms,
Lies the Cullinane diamond theorem,
A structure that transforms.

Four-diamond figure, a 4×4 array,
Of two-color diagonally-divided square tiles,
Permutations of these sixteen,
In rows, columns, and quadrants compiles.

Every G-image of the four-diamond figure,
Has some ordinary or color-interchange symmetry,
A pattern, a structure, a mathematical picture,
A testament to geometry's clarity.

The symmetry of the line diagrams,
Accounts for the symmetry of the two-color patterns,
A proof shows that a 2nx2n two-color triangular half-squares pattern,
Must have a 2×2 center with a symmetry that matters.

And this symmetry must be shared by the entire pattern,
A statement, a theorem, a mathematical lantern,
G is isomorphic to the affine group A,
On the linear 4-space over GF (2), they say.

The 35 structures of the 840 = 35 x 24 G-images,
Are isomorphic to the 35 lines,
In the 3-dimensional projective space over GF (2),
A concept that shines.

So here lies the beauty of the Cullinane diamond theorem,
In the mind of the mathematician, it's a gem,
A structure, a pattern, a mathematical diagram,
A testament to the beauty of STEM.