See the web pages octad.group and octad.us.
Related geometry (not the 759 octads, but closely related to them) —
#/media/File:150614-PG-3-2-schoolgirls-arrangement.png)
The 4×6 rectangle of R. T. Curtis
illustrates the geometry of octads —
Curtis splits the 4×6 rectangle into three 4×2 "bricks" —
.
"In fact the construction enables us to describe the octads
in a very revealing manner. It shows that each octad,
other than Λ1, Λ2, Λ3, intersects at least one of these ' bricks' —
the 'heavy brick' – in just four points." . . . .
— R. T. Curtis (1976). "A new combinatorial approach to M24,"
Mathematical Proceedings of the Cambridge Philosophical Society ,
79, pp 25-42.