The Ninth* Configuration 

The ninth in a list of configurations—

"There is a (2^d-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.