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Thursday, April 23, 2020

Octads and Geometry

Filed under: General — Tags: , , — m759 @ 10:11 PM

See the web pages octad.group and octad.us.

Related geometry (not the 759 octads, but closely related to them) —


The 4×6 rectangle of R. T. Curtis
illustrates the geometry of octads —

Counting symmetries with the orbit-stabilizer theorem

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). “new combinatorial approach to M24,”
Mathematical Proceedings of the Cambridge Philosophical Society ,
79, pp 25-42.

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