This paper introduces a novel six-dimensional (6D) movable antenna (6DMA) system for future wireless networks to enhance communication performance. Unlike traditional fixed-position antennas (FPAs) and existing fluid antenna/two-dimensional (2D) movable antenna (FA/2DMA) systems, the 6DMA system consists of distributed antenna surfaces that can independently adjust their 3D positions and rotations within a given space. The 6DMA system is applied to base stations (BSs) to provide full degrees of freedom (DoFs) for adapting to dynamic user spatial distributions. The main challenge is to optimize the 6D positions and rotations of all 6DMA surfaces to maximize network capacity while considering practical constraints. The paper models the 6DMA-enabled BS and user channels, formulates an optimization problem, and proposes an alternating optimization algorithm using Monte Carlo simulation. Numerical results demonstrate that the proposed 6DMA-BS significantly improves network capacity compared to benchmark BS architectures with FPAs or MAs, especially in non-uniform user distributions.This paper introduces a novel six-dimensional (6D) movable antenna (6DMA) system for future wireless networks to enhance communication performance. Unlike traditional fixed-position antennas (FPAs) and existing fluid antenna/two-dimensional (2D) movable antenna (FA/2DMA) systems, the 6DMA system consists of distributed antenna surfaces that can independently adjust their 3D positions and rotations within a given space. The 6DMA system is applied to base stations (BSs) to provide full degrees of freedom (DoFs) for adapting to dynamic user spatial distributions. The main challenge is to optimize the 6D positions and rotations of all 6DMA surfaces to maximize network capacity while considering practical constraints. The paper models the 6DMA-enabled BS and user channels, formulates an optimization problem, and proposes an alternating optimization algorithm using Monte Carlo simulation. Numerical results demonstrate that the proposed 6DMA-BS significantly improves network capacity compared to benchmark BS architectures with FPAs or MAs, especially in non-uniform user distributions.