Diamond theory
This page has been listed on . Please see that page for justifications and discussion.
Diamond theory is the theory of affine groups over GF(2) acting on small square and cubic arrays. In the simplest case, the symmetric group of degree 4 acts on a two-colored diamond figure like that in Plato's Meno dialogue, yielding 24 distinct patterns, each of which has some ordinary or color-interchange symmetry.
This symmetry-invariance can be generalized to (at least) a group of order approximately 1.3 trillion acting on a 4x4x4 array of cubes.
The theory has applications to finite geometry and to the construction of the large Witt design underlying the Mathieu group of degree 24.
External link
Referenced By
List of mathematical topics (D-F) | List of mathematical topics (F-Z)
|
