Investigation of the spatial organization of large-scale, coherent structures in turbulent, Rayleigh-Bénard convection is performed through direct numerical simulation. The simulation is performed in a 6.3 aspect ratio cell with a Rayleigh number of 9.6 × 107 and Prandtl number equal to 6.7. Single and double point statistics are compared against experimental results and are found to be in excellent agreement. Large-scale mean thermals with coherence times exceeding 10 eddy-turnovers are discovered and these mean thermals are found to be a reliable tool for identifying and interpreting the large, velocity roll-cells. Our simulations show an existence of a large-scale coherent pattern that consists of three major velocity roll-cells, two of which are semi-toroidal, or horse-shoe shaped, that are connected to the side-walls, and the third roll-cell lies across the center of the cell between the semi-toroidal cells. We present the possible formation mechanism of this nearly-periodic structure, observed at intermediate scales of averaging, as a perturbation from a perfectly periodic, crystal-like, pattern. The dynamics of these structures are evaluated using short-time averages.