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