Table 6 Magic formulas for the bcc cuboctahedron
From: Magic Mathematical Relationships for Nanoclusters—Errata and Addendum
bcc cuboctahedron | ||
---|---|---|
| Atoms | \(\frac {5}{3}n^{3}+7n^{2}+\frac {34}{3}n+7,~n\ge 1\) odd |
\(\frac {5}{3}n^{3}+7n^{2}+\frac {25}{3}n+1,~n\ge 2\) even | ||
Bonds | \(\frac {20}{3}n^{3}+19n^{2}+\frac {64}{3}n+9,n\ge 1\) odd | |
\(\frac {20}{3}n^{3}+19n^{2}+\frac {46}{3}n,~n\ge 2\) even | ||
cn=2 | 12, n≥1 odd; 0, n even | |
cn=3 | 12n−12, n≥1 odd; 0, n even | |
cn=4 | 4n2−4n+6, n≥1 odd | |
4n2+8n, n≥2 even | ||
cn=6 | 0, n≥1 odd; 12, n even | |
cn=7 | 2n2+4n+2, n≥1 odd | |
2n2+4n−16, n≥2 even | ||
cn=8 | \(\frac {5}{3}n^{3}+1n^{2}-\frac {2}{3}n-1,~n\ge {1}\) odd | |
bcc cuboctahedron n=2 | \(\frac {5}{3}n^{3}+1n^{2}-\frac {11}{3}n+5,~n\ge {2}\) even |