Click image for some background.

Shown above is a rearranged version of the

Miracle Octad Generator (MOG) of R. T. Curtis

("A new combinatorial approach to M_{24},"

*Math. Proc. Camb. Phil. Soc*., 79 (1976), 25-42.)

The 8-subcell rectangles in the left part of the figure may be

viewed as illustrating (if the top left subcell is disregarded)

the thirty-five 3-subsets of a 7-set.

Such a view relates, as the remarks below show, the

MOG's underlying Galois geometry, that of PG(3,2), to

the *hexagrammum mysticum * of Pascal.

**On Danzer's 35**_{4} Configuration:

"Combinatorially, Danzer’s configuration can be interpreted

as defined by all 3-sets and all 4-sets that can be formed

by the elements of a 7-element set; each 'point' is represented

by one of the 3-sets, and it is incident with those lines

(represented by 4-sets) that contain the 3-set."

— Branko Grünbaum, "Musings on an Example of Danzer's,"

*European Journal of Combinatorics* , 29 (2008),

pp. 1910–1918 (online March 11, 2008)

"Danzer's configuration is deeply rooted in

Pascal's *Hexagrammum Mysticum* ."

— Marko Boben, Gábor Gévay, and Tomaž Pisanski,

"Danzer's Configuration Revisited," arXiv.org, Jan. 6, 2013

For an approach to such configurations that differs from

those of Grünbaum, Boben, Gévay, and Pisanski, see

Classical Geometry in Light of Galois Geometry.

Grünbaum has written little about Galois geometry.

Pisanski has recently touched on the subject;

see Configurations in this journal (Feb. 19, 2013).