Table 4 Magic formulas for the bcc truncated octahedron
From: Magic Mathematical Relationships for Nanoclusters—Errata and Addendum
bcc truncated octahedron | ||
|---|---|---|
| n odd | |
Atoms | \(8n^{3}+\frac {9}{2}n^{2} +\frac {5}{2},~n\ge 1\) odd | |
Bonds | 32n3−6n2+6, n≥1 odd | |
cn=4 | 9n2+5,n≥1 odd | |
cn=6 | 6n−6, n≥1 odd | |
cn=7 | 12n2−12n, n≥1 odd | |
cn=8 | \(8n^{3}-\frac {33}{2}n^{2}+6n+\frac {7}{2},~n\ge {1}\) odd | |
n even | ||
Atoms | \(8n^{3}+\frac {9}{2}n^{2} +3n+1,~n\ge 2\) even | |
Bonds | 32n3−6n2, n≥2 even | |
cn=2 | 6n+12, n≥2 even | |
cn=3 | 12n−24, n≥2 even | |
cn=4 | 9n2−18n+14,n≥2 even | |
cn=6 | 6n, n≥2 even | |
cn=7 | 12n2−12n, n≥2 even | |
bcc truncated octahedron n=2 | cn=8 | \(8n^{3}-\frac {33}{2}n^{2}+9n-1,~n\ge {2}\) even |
