Finite
Geometry
Notes

The Ninth* Configuration
The ninth in a list of configurations—
"There
is a (2^{d1})_{d}
configuration
known as the Cox configuration."
— MathWorld article on "Configuration"
For
futher details on the Cox 32_{6} configuration's
Levi graph,
isomorphic to the sixdimensional hypercube γ_{6
}, see
Coxeter, "SelfDual
Configurations and Regular Graphs,"
Bull. Amer. Math. Soc. Vol. 56, pages
413455, 1950.
This contains a discussion of Kummer's 16_{6} as it
relates to γ_{6 },
another form of the 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 11_{3}
configurations is counted
as seventh— and then the
ninth would
be a 15_{
3} and
some related material would be Inscapes.