  The exact symmetry identities among four-point tree-level amplitudes of
bosonic open string theory as derived by G. W. Moore are re-examined. The main
focuses of this work are: (1) Explicit construction of kinematic configurations
and a new polarization basis for the scattering processes. These setups
simplify greatly the functional forms of the exact symmetry identities, and
help us to extract easily high-energy limits of stringy amplitudes appearing in
the exact identities. (2) Connection and comparison between D. J. Gross's
high-energy stringy symmetry and the exact symmetry identities as derived by G.
W. Moore. (3) Observation of symmetry patterns of stringy amplitudes with
respect to the order of energy dependence in scattering amplitudes.
