Suppose that a base cuboid has three dimensions, \(A, B, C\), with the following number of cells: \(|A|=1,000,000,|B|=100\), and \(|C|=1000\). Suppose that each dimension is evenly partitioned into 10 portions for chunking.

a. Assuming each dimension has only one level, draw the complete lattice of the cube.

b. If each cube cell stores one measure with four bytes, what is the total size of the computed cube if the cube is dense?

c. State the order for computing the chunks in the cube that requires the least amount of space, and compute the total amount of main memory space required for computing the 2-D planes.