Some perfect cones
In a given dimension n, there are only a finite number of orbits of perfect cones of rank k.
In order to solve the problem considered in
Smoothness and singularities of the perfect form compactification of Ag
we needed to enumerate the perfect cones of rank up to 9.
The perfect cones of dimension n and rank n correspond to certain configurations of shortest vectors and are enumerated for dimension n<=9 in
On classifying Minkowskian sublattices
and references therein.
The faces of the cones of dimension at most 7 are enumerated in
Perfect forms and the cohomology of modular groups
The faces of rank 9 and dimension 8 are enumerated in
Smoothness and singularities of the perfect form compactification of Ag
.
Merged data set is available at
DATApaper.tar.gz
. Data can be read in GAP by doing ReadAsFunction(File)() with File one of the files of the archive.