We analyze achievable multiplexing gains (MUXGs) of fully connected K-user line-of-sight (LOS) interference channels (ICs). An array of polarimetric antennas, each composed of three orthogonal electric dipoles and three orthogonal magnetic dipoles in which all six elements are co-located, is used throughout this paper. For a K-user LOS IC with single polarization, the maximum achievable MUXG is only K, regardless of the number of transmit and receive antennas at each node due to the key-hole effect. If polarimetric antennas are used at each node, a trivial upper bound on the MUXG is now 2K. In this paper, we consider zero-forcing (ZF) and interference alignment (IA) schemes to achieve this upper bound. We show the optimal MUXG of 2K is achievable if M >= inverted right perpendicularK+1/6inverted left perpendicular polarimetric antennas are used at each node for any K. In addition, using the proposed ZF scheme, we obtain minimal dipole configurations at each node that achieve this upper bound for K < 5. Furthermore, we analyze achievable MUXGs using the distributed interference alignment (DIA) algorithm. Although IA can generally provide a higher MUXG than ZF for LOS ICs, we observe that the number of required dipole elements to achieve the optimal MUXG of 2K under a ZF scheme is the same as that required under IA for all cases we consider.