Reflexive polyhedra in 3 dimensions
This is a
list of all 4319
reflexive polyhedra in 3 dimensions (
hep-th/9805190
).
The file is in the PALP-compatible format
# # M:# # N:# # Pic:# Cor:#
followed by 3 lines with the coordinates of the vertices,
where the numbers indicated by # stand for
dimension (=3) and number of vertices (as needed by PALP),
point and vertex numbers in the M lattice,
point and vertex numbers in the N lattice,
Picard number and correction term.
The Picard numbers of a polyhedron and of its dual add up to 20 + correction (=last term in eq. (4) of hep-th/9805190).
There are the following
116 (C)WS
and 16 r-maximal polytopes. For explanations see
CS/WS
.
95
single WS
17
CWS
of the type 3+3 (non-trivial)
The 4 CWS from combining the (C)WS (1, 1, 1), (1, 1, 2), (1, 2, 3) and (1, 1, 0, 0; 0, 0, 1, 1) for d=2 trivially with (1,1)
15 of the above are
r-minimal (C)WS
The 16'th r-maximal polytope is given by
3 4 1 1 1 -3 0 2 0 -2 0 0 4 -4