Lm.pdb

# These are the vectors in Schiemann's S1 lattice of length <= sqrt(8).

# This is (loosely) a Protein Data Bank format file.
# <https://en.wikipedia.org/wiki/Protein_Data_Bank_(file_format)>

# I tried to find an embedding with rational coordinates, but I don't think
# it's possible. Here I use sqrt(7) = 2.6458.


# To verify correctness, note that the Gram matrix can be generated in PARI/GP
# following command based on this script:
# <https://gist.githubusercontent.com/maresb/4ccc43ce07bc9e44e031aa9837a5104f/raw/schiemann.gp>

#  colvectors_ALm~ * ALm * colvectors_ALm

#     [ 8 -6 2]
#     [-6  8 2]
#     [ 2  2 4]

# It can be verified that the Gram matrix is correct with respect to the coordinates
# of atoms 6, 4, 2.

ATOM      1  A   HIS A   1      0.0000  0.0000  0.0000  1.00 25.00           C
ATOM      2  D   HIS A   1      0.0000  2.0000  0.0000  1.00 25.00           S
ATOM      3  D   HIS A   1      0.0000 -2.0000  0.0000  1.00 25.00           S
ATOM      4  B   HIS A   1      2.6458  1.0000  0.0000  1.00 25.00           O
ATOM      5  C   HIS A   1     -2.6458 -1.0000  0.0000  1.00 25.00           O
ATOM      6  G   HIS A   1     -2.6458  1.0000  0.0000  1.00 25.00           O
ATOM      7  F   HIS A   1      2.6458 -1.0000  0.0000  1.00 25.00           O

CONECT 1    2    3    4
CONECT 1    5    6    7