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Table 16 Magic formulas for the hexagonal bipyramid
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From: Magical Mathematical Formulas for Nanoboxes

Hexagonal bipyramid

Atoms

\((12t)n^2+(-12t^2+12t)n+(4t^3-6t^2+4t), \,n>t\ge 2\)

Bonds

\((72t-42)n^2+(-72t^2+114t-42)n+(24t^3-57t^2+45t-12),\,n>t\ge 2\)

cn = 3

\(2,\,n>t\ge 2\)

cn = 5

\(6,\,n>t\ge 2\)

cn = 6

\(3n+3,\,n>t\ge 2\)

cn = 7

\((24)n - 24,\,n>t\ge 2\)

cn = 8

\(12n^2+(-12t-15)n + (6t^2+9),\,n>t\ge 2\)

cn = 9

\(12n^2+(-12t-18)n+(6t^2+6t+6),\,n>t\ge 2\)

cn = 10

\(30n+(-30t),\,n>t\ge 2\)

cn = 11

\(12,\,n>t\ge 2\)

cn = 12

\((12t-24)n^2 +(-12t^2+36t-124)n+(4t^3-18t^2+28t-14),\,n>t\ge 2\)

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