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