  For the first time, we have introduced the Pyramid Constellation of
Gravitational Wave Observatory (PCGO) for GW polarization detection. The PCGO
is composed of four identical spacecrafts (S/Cs). The laser telescopes and
their pointing structures are mounted on the S/C platform and are evenly
distributed at three locations 120 degrees apart. Compared to a three-S/C
configuration, the addition of a fourth S/C and its mounted telescope serve as
redundant backups, especially for the telescopes, which together with the other
two telescopes, automatically form a stable mass center for the platform
without the need for trim mass. Since the radial distance of S/C4 is greater
than that of the other spacecraft, the three arm lengths associated with S/C4
change significantly over a one-year period. Time delay interferometry (TDI)
has been proven effective for suppressing frequency noise in this context. The
unequal arm Michelson TDI configuration and the Sagnac TDI configuration are
equally effective for eliminating the laser frequency noise based on the PCGO
configuration. Compared to the configurations of LISA, Taiji, and TianQin, the
PCGO has more combinations of optical paths in its TDI system, offering greater
sensitivity to GW signals. The configuration of PCGO is simultaneously
sensitive to the six polarization modes of GWs, which means that it allows for
greater flexibility in extracting the polarization components from the total GW
polarization signals.
