The Pyramidic or Half-Octahedral geometry is not derived for any other purpose other than the fact I was able to create this structure using Combinatorics, via this equation that uses only whole integers.

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


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The algebraic equation corresponding:

The algebraic equation corresponding:

















Several angles expressing: sum total = 52 = 25, Pyramidic
Several angles expressing: sum total = 53 = 125, Pyramidic
Several angles expressing: sum total = 54 = 625 ; Pyramidic
Several angles expressing: sum total = 55 = 3,125 ; Pyramidic
Several angles expressing: sum total = 56 = 15,625 ; Pyramidic
Several angles expressing: sum total = 57 = 78,125 ; Pyramidic, central focus
Several angles expressing: sum total = 58 = 390,625 ; Pyramidic, central focus