**In the Miracle Octad Generator (MOG):**

The above details from a one-page note of April 26, 1986, refer to the

Miracle Octad Generator of R. T. Curtis, as it was published in 1976:

From R. T. Curtis (1976). A new combinatorial approach to M_{24},

*Mathematical Proceedings of the Cambridge Philosophical Society *,

**79**, pp 25-42. doi:10.1017/S0305004100052075.

The 1986 note assumed that the reader would be able to supply, from the

MOG itself, the missing top row of each heavy brick.

Note that the interchange of the two squares in the top row of each

heavy brick induces the diamond-theorem correlation.

Note also that the 20 pictured 3-subsets of a 6-set in the 1986 note

occur as *paired complements* in two pictures, each showing 10 of the

3-subsets.

This pair of pictures corresponds to the 20 *Rosenhain tetrads* among

the 35 lines of PG(3,2), while the picture showing the 2-subsets

corresponds to the 15 *Göpel tetrads* among the 35 lines.

See Rosenhain and Göpel tetrads in PG(3,2). Some further background: