The Cube, taken first as a basic Platonic Solid, of course has been known for all eternity by all knowledge-holders,

at any rate, it is the most boring of the shapes because it is so familiar, and it is used everywhere in design.

In terms of Combinatorics, it is a rather simple pattern, just Pascal's Triangle to the third power.

  (N!)         (N!)         (N!)  
X!(N-X)! Y!(N-Y)! Z!(N-Z)!

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An expression for the cube as an open-form algebra is ((A+B)(C+D)(E+F))N, what isn't any less efficient than (A+B+C+D)N, though that I feel should be reserved for the Tetrahedral Pascalloid.

Both pascalloids and indeed all pascalloids begin with a unit [1], that is in some cases times 10x.

Here we have the cubic algorythm, eight variables that add spread across three dimensional space of zeros.

At unit N = 1, we say 8N=1, and this is significant, so then let us visualize what may iterate from that.

Two expressions of ((A+B)(C+D))N at N=1, or sum total 81 = 8
Three visualizations of the Cubic Pascalloid at N = 2, sum total 82 = 64
Three visualizations of the Cubic Pascalloid at N = 3, sum total 83 = 512
Three visualizations of the Cubic Pascalloid at N = 4, sum total 84 = 4,096
Four visualizations of the Cubic Pascalloid at N = 5, sum total 85 = 32,768
Three central visualizations of the Cubic Pascalloid at N = 6, sum total 86 = 262,144
Four central visualizations of the Cubic Pascalloid at N = 7, sum total 87 = 2,097,152

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