Classifications of magnetized T4 and T4/Z2 orbifold models

We study constructions and classifications of three-generation models based on magnetized $T^4$ $T^4/{Z}_2$ orbifold as candidates the compact space. focus chiral fermion zero-mode wave functions in extra dimensions. Freedoms constant gauge fields, called Scherk-Schwarz phases are taken into account. Infinite number yielded, corresponding to ways which magnetic flux can be turned on. classify them a systematic manner, clarifying relationship between different models. The Higgs sector is also studied by analyzing possible assignments phases, etc. left- right-handed fermions.