关键词：正则同伦；非定向表面
摘 要：This is a revised and extended version of Tech Report (EECS-2012-200) with the same title. The construction of various Klein bottles that belong to different regular homotopy classes, and which thus cannot be smoothly transformed into one another, is formally introduced. For all cases it is shown how these shapes can be partitioned into two Mobius bands and how the twistedness of these bands defines the homotopy type.