An infinite family of Gromoll-Meyer spheres
  We construct a new infinite family of models of exotic 7-spheres. These models are direct generalizations of the Gromoll-Meyer sphere. From their symmetries, geodesics and submanifolds half of them are closer to the standard 7-sphere than any other known model for an exotic 7-sphere. 
C. Duran, T. Puettmann, A. Rigas