This paper studies the exploitation of triple polarization (TP) for multi-user (MU) holographic multiple-input multiple-output surface (HMIMOS) wireless communication systems, aiming at capacity boosting without enlarging the antenna array size. We specifically consider that both the transmitter and receiver are equipped with an HMIMOS comprising compact sub-wavelength TP patch antennas. To characterize TP MUHMIMOS systems, a TP near-field channel model is proposed using the dyadic Green's function, whose characteristics are leveraged to design a user-cluster-based precoding scheme for mitigating the cross-polarization and inter-user interference contributions. A theoretical correlation analysis for HMIMOS with infinitely small patch antennas is also presented. According to the proposed scheme, the users are assigned to one of the three polarizations, which is easy to implement, at the cost, however, of reducing the system's diversity. Our numerical results showcase that the cross-polarization channel components have a nonnegligible impact on the system performance, which is efficiently eliminated with the proposed MU precoding scheme.