  The dual configuration of the original one is proposed for the orbit design
of Taiji spacecrafts. In terms of these two configurations of Taiji, an
algorithm is devised to expand the unperturbed Keplerian orbits of spacecrafts
to infinite order of $e$, the orbital eccentricity, in the heliocentric
coordinate system. Further, based on the algorithm, all the kinematic
indicators of Taiji triangles, say three arm-lengths and their corresponding
rates of change, and three vertex angles, in both configurations are also be
expanded to infinite order of $e$, and it is proved that both configurations of
Taiji possess the same symmetry: At every order, three components of every
kinematic indicator of Taiji triangle are identical to each other up to a phase
shift of $2\pi/3$, which is independent on the tilt angle of Taiji plane
relative to the ecliptic plane. Finally, the above algorithm is slightly
modified, and with it, by adjusting the tilt angle around $\pi/3$ to any order
of $e$, the orbits of Taiji spacecrafts in each configuration can be optimized.
