How do I convert from the upper notation to the lower notation in the simulation box?

LAMMPS LAMMPS Beginners
1

ITEM: BOX BOUNDS xy xz yz pp pp pp
0.0000000000000000e+00 3.6856347799999995e+01 0.0000000000000000e+00
0.0000000000000000e+00 5.2970990000000002e+00 1.0420814300000000e+01
0.0000000000000000e+00 2.5465293899999999e+01 0.0000000000000000e+00
ITEM: ATOMS type x y z
1 1.97227 4.41897 3.6125
2 1.74508 0.876347 3.04686
2 3.16301 3.53151 2.44012

How do I convert from the upper notation to the lower notation in the simulation box?

CELL_PARAMETERS (angstrom)
24.466252 0.000000 10.011990
0.000000 5.297099 0.000000
0.000000 0.000000 27.514988

ATOMIC_POSITIONS (angstrom)
Si 0.222432673 4.336077926 13.84452182
C 0.298591826 0.852957123 13.74224196
C 0.310974039 4.438328151 11.0427127

2

You can use VMD to read the data file (read the topotools manual for documentation):

vmd > topo readlammpsdata yourfile.data full

Or better, you can use the LAMMPS manual and study section 8.2.3 Triclinic (non-orthogonal) simulation boxes, which contains all the relevant formulas.

3

Add suppport for general triclinic simulation boxes and systems by sjplimp · Pull Request #3984 · lammps/lammps · GitHub may also be related (not yet merged into public LAMMPS).