  The quasiparticle band structures of four polytypes 3C, 6H, 4H, and 2H of
GaP, GaAs, GaSb, InP, InAs, and InSb are computed with high accuracy including
spin-orbit interaction applying a recently developed approximate calculation
scheme, the LDA-1/2 method. The results are used to derive band offsets
  $\Delta E_c$ and $\Delta E_v$ for the conduction and valence bands between
two polytypes. The alignment of the band structures is based on the
branch-point energy
  $E_{\rm BP}$ for each polytype. The aligned electronic structures are used to
explain properties of heterocrystalline but homomaterial junctions.
  The gaps and offsets allow to discuss spectroscopic results obtained recently
for such junctions in III-V nanowires.
