The 48-Variable Rhombicuboctahedron is an Octagonal pascalloid scaled to N, transformed into a diagonal orientation along the 'y' axis, then summed across the three dimensions of a cube (scaled also to N). The structure was impossible to fit into Excel, as it requires seven dimensions of work-space to be filled with index number strings and relative referenced Combinatoric Equations.

The summation is over a standard pascalloid cube made of three Pascal's Triangle dimensions as before, but this is multiplied by the part that is Octahedral and diagonally rotated, making a checkerboard of numbers and thus a requisite of 'even numbers only' for this multi-dimensional checkerboard.

Expression for the 48-Variable Rhombicuboctahedron:

Given (X+Y+Z+W) is Even,



No Excel proof yet complete

This interesting calculation produces results that an 'elongated box'. Now we have the algebraic solution that produces these numbers as well.



The geometry is still n-based, starting here at N=1. It is viewable here up to N=5

481 = 48
482 = 2,304
483 = 110,592
484 = 5,308,416