The Diamond Connection:
From Quilt Blocks to the
Mathieu Group M24
Click on illustrations for details.
The four-diamond figure is related to the finite geometry PG(3,2). (See "Symmetry Invariance in a Diamond Ring," AMS Notices, February 1979, A193-194.) PG(3,2) is in turn related to the 759 octads of the Steiner system S(5,8,24). (See "Generating the Octad Generator," expository note, 1985.)
For the connection of S(5,8,24) with the Mathieu group M24, see the references in The Miracle Octad Generator.