The 15 2-subsets of a 6-set correspond to the 15 points of PG(3,2).

(Cullinane, 1986*)

The 35 3-subsets of a 7-set correspond to the 35 lines of PG(3,2).

(Conwell, 1910)

The 56 3-subsets of an 8-set correspond to the 56 spreads of PG(3,2).

(Seidel, 1970)

Each correspondence above may have been investigated earlier than

indicated by the above dates , which are the earliest I know of.

See also Correspondences in this journal.

* The above 1986 construction of PG(3,2) from a 6-set also appeared

in the work of other authors in 1994 and 2002 . . .

- Gonzalez-Dorrego, Maria R. (Maria del Rosario),

*(16,6) Configurations and Geometry of Kummer Surfaces in*P^{3}.

American Mathematical Society, Providence, RI, 1994. - Dolgachev, Igor, and Keum, JongHae,

“Birational Automorphisms of Quartic Hessian Surfaces.”

Trans. Amer. Math. Soc.**354**(2002), 3031-3057.

Addendum at 5:09 PM suggested by an obituary today for Stephen Joyce:

See as well the word *correspondences* in

“James Joyce and the Hermetic Tradition,” by William York Tindall

(*Journal of the History of Ideas* , Jan. 1954).