Exercise: The eight-part diagrams in the graphic "brick space"
model of PG(5,2) below need to be suitably labeled with six-part
GF(2) coordinates to help illustrate the Klein correspondence that
underlies the large Mathieu group M24.
.gif)
A possible approach: The lines separating dark squares from light
(i.e., blue from white or yellow) in the figure above may be added
in XOR fashion (as if they were diamond theorem line diagrams)
to form a six dimensional vector space, which, after a suitable basis
is chosen, may be represented by six-tuples of 0's and 1's.
Related reading —
log24.com/log24/241221-'Brick Space « Log24' – m759.net.pdf .
This is a large (15.1 MB) file. The Foxit PDF reader is recommended.
The PDF is from a search for Brick Space in this journal.
Some context: http://m759.net/wordpress/?s=Weyl+Coordinatization.