From Peter Shor (AT&T Bell Labs): shor@research.att.com

Here is my generator for Keller graphs.  These graphs come from attempts
at computer disproofs of Keller's conjecture (and were defined first by
Corradi and Szabo).  There's a size parameter (SIZE) defined in the 
program, and the most interesting case is probably when it's set to 6.  
For SIZE=6, I have found a large clique (by "hand") which is larger than 
any computer program has found so far.  For 5 or less, computer programs 
have found the largest clique, so we know what it is.  For SIZE=7, the 
graph is probably too big to put in the DIMACS challenge (14000 nodes, and 
reasonably dense).  I would recommend putting at least the SIZE=5 and 
SIZE=6 graphs in.  The SIZE=4 graph might be too small (Only 171 nodes, 
and the largest clique is size 11).  

Anyway, if somebody finds a clique larger than 59 vertices for 
SIZE=6, I'd be interested.

Also, I might be able to supply more graphs derived from Keller's 
conjecture.  Tell me how these are working.

References:

J.C. Lagarias and P.W. Shor, "Keller's cube-packing conjecture is
false in high dimensions," Bull. AMS (New Series), Vol. 27, No. 2,
279-283, 1992.

K Corradi and S Szabo, "A combinatorial approach for Keller's conjecture,"
Period. Math. Hungar. Vol. 21, 91-100, 1990.

Further update:

The clique size for the 5-graph is 27.

For the 7-graph (if anybody actually tries it), I know the clique size
is between 123 and 127.  The clique size is 2^n-1 for n >= 10, but these
graphs are much too big to even write down.