Just as the 8-axis functions as the structural fulcrum for the two-dimensional matrix, the construction of the three-dimensional cube matrix is reliant upon this same foundation. The process of determining the organization of matrices in a three-dimensional space was made simpler by first constructing an "inner" framework of axes within the cube. The start and end points for each axis would coincide with the start or end point of another to form a basic scaffold upon which the matrices would be applied. The position and orientation of each of these axes would eventually correspond to the primary axes for each matrix. For the purpose of analysis, this framework has been placed within a semi-transparent cube, and gradually rotated to better display its structure.

Once the structure of the primary axes has been established, the same matrix is "mapped" onto each surface of the cube according to the orientation of each axis. One method is by "reflecting" each successive matrix around the vertical faces of the cube until only the horizontal faces - top and bottom - are left. An important point to consider during the process of construction is the placement of the last two sides - in this case, top and bottom. While all the units along the outer boundaries for the four other matrices coincide, the last two sides of the cube rely both upon identical units, and paired units (1 and 6, 2 and 5, 3 and 4, 7 and 9) to complete the cube. The nature of the matrix itself prevents every numerical value along the boundary from coinciding exactly, but since each unit is one of a pair - as discussed in the previous section - the twin can perform the same function. By lining up the start and end points of each 8-axis, therefore, the two remaining faces of the cube are completed with both identical and paired units forming the boundaries.

Taking into account the fact that each numerical value within the matrix has a frequency, a cycle duration, and an amplitude, the compositional possibilities increase exponentially with the introduction of a third dimension. While the properties of a unit within a matrix are no different from those of a corresponding unit in a matrix on another side of the cube, the potential for variation is enormous, since any number of parameters could be used to define them, not just those used here. Trigonometry, volumetrics, and structural mechanics are somewhat beyond the scope of this study, for ultimately the purpose of the cube matrix is a creative one, not a mathematical one. For the purpose of a composition, therefore, I will investigate two possibilities for the introduction of modifiers into this model.