On Lattices Equivalent to Their Duals*

J. H. Conway 
Mathematics Department 
Princeton University 
Princeton, NJ 08544 USA 

N. J. A. Sloane (*)
Mathematical Sciences Research Center 
AT&T Bell Laboratories 
Murray Hill, New Jersey 07974 USA 

(*) Present address:
Information Sciences Research
AT&T Shannon Lab
Florham Park, NJ 07932-0971 USA
Email: njas@research.att.com


ABSTRACT

A lattice is called isodual if it is geometrically congruent to its dual.
We show that the densest three-dimensional isodual lattice is the
``central centered-cuboidal'' lattice, a lattice which
is in a sense the mean of the face-centered and body-centered
cubic lattices.  This lattice is also the most economical
three-dimensional isodual covering.  We give a number of
other dense isodual lattices in R^n, n <= 24.


A different version of this paper appeared in Journal of Number Theory,
48 (1994), 373-382.
It is also DIMACS Technical Report 93-88, December 1993.


For the full version see
http://www.research.att.com/~njas/doc/isodual.pdf (pdf) or
http://www.research.att.com/~njas/doc/isodual.ps (ps)