This paper investigates the utilization of triple polarization (TP) for multi-user (MU) holographic multiple-input multi-output surface (HMIMOS) wireless communication systems, targeting capacity boosting and diversity exploitation without enlarging the antenna array sizes. We specifically consider that both the transmitter and receiver are both equipped with an HMIMOS consisting of compact sub-wavelength TP patch antennas within the near-field (NF) regime. To characterize TP MU-HMIMOS systems, a TP NF channel model is constructed using the dyadic Green's function, whose characteristics are leveraged to design two precoding schemes for mitigating the cross-polarization and inter-user interference contributions. Specifically, a user-cluster-based precoding scheme assigns different users to one of three polarizations at the expense of the system's diversity, and a two-layer precoding scheme removes interference using the Gaussian elimination method at a high computational cost. The theoretical correlation analysis for HMIMOS in the NF region is also investigated, revealing that both the spacing of transmit patch antennas and user distance impact transmit correlation factors. Our numerical results show that the users far from transmitting HMIMOS experience higher correlation than those closer within the NF regime, resulting in a lower channel capacity. Meanwhile, in terms of channel capacity, TP HMIMOS can almost achieve 1.25 times gain compared with dual-polarized HMIMOS, and 3 times compared with conventional HMIMOS. In addition, the proposed two-layer precoding scheme combined with two-layer power allocation realizes a higher spectral efficiency than other schemes without sacrificing diversity.