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Notes by Steven H. Cullinane on February 14, 2012:

The Ninth* Configuration 

The ninth in a list of configurations—

"There is a (2d-1)d  configuration
  known as the Cox configuration."

— MathWorld article on "Configuration"

For futher details on the Cox 326 configuration's Levi graph,
isomorphic to the six-dimensional hypercube γ6  , see 
Coxeter, "Self-Dual Configurations and Regular Graphs,"
Bull. Amer. Math. Soc.  Vol. 56, pages 413-455, 1950.
This contains a discussion of Kummer's 166 as it
relates to  γ6  , another form of the 4×4×4 Galois cube.

See also Solomon's Cube.

* Title inspired by the novel of William Peter Blatty.
Note that Cox configurations are Tenth,  if the fleeting
MathWorld reference to 113 configurations is counted
as seventh—  and then the ninth  would be a 15 3 and
some related material would be Inscapes.

 

be a 15 3 and
some related material would be Inscapes.