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The dual configuration of the original one is proposed for the orbit designof Taiji spacecrafts. In terms of these two configurations of Taiji, analgorithm is devised to expand the unperturbed Keplerian orbits of spacecraftsto infinite order of $e$, the orbital eccentricity, in the heliocentriccoordinate system. Further, based on the algorithm, all the kinematicindicators of Taiji triangles, say three arm-lengths and their correspondingrates of change, and three vertex angles, in both configurations are also beexpanded to infinite order of $e$, and it is proved that both configurations ofTaiji possess the same symmetry: At every order, three components of everykinematic indicator of Taiji triangle are identical to each other up to a phaseshift of $2\pi/3$, which is independent on the tilt angle of Taiji planerelative to the ecliptic plane. Finally, the above algorithm is slightlymodified, and with it, by adjusting the tilt angle around $\pi/3$ to any orderof $e$, the orbits of Taiji spacecrafts in each configuration can be optimized.

Analytical analysis on the orbits of Taiji spacecrafts to infinite order of the orbital eccentricity