Object | N | N’ | Analytical Equation | Analytical Result | \( {\displaystyle \sum_{i=1}^N\left|{\overrightarrow{S}}_i\right|} \) | \( {\displaystyle \sum_{i=1}^{N^{\prime }}\left|{\overrightarrow{A}}_i\right|} \) |
---|---|---|---|---|---|---|
Octahedron | 6 | 8 | \( 4\sqrt{3}{R}^2 \) | 6.92820 | 6.92820 | 6.92820 |
Icosahedron | 12 | 20 | \( {\scriptscriptstyle \frac{40\sqrt{3}}{5+\sqrt{5}}}{R}^2 \) | 9.57454 | 9.57454 | 9.57454 |
≈ Sphere | 642 | 1280 | ≈ 4πR ^{2} | 12.5664 | 12.5037 | 12.5065 |