The formula to calculate the Surface to Volume Ratio (RA/V) of an Octahedron given the Space Diagonal (dSpace) is:
\[ RA/V = \frac{6 \sqrt{3}}{d_{Space}} \]
Where:
The Surface to Volume Ratio of an Octahedron is the numerical ratio of the total surface area to the volume of the Octahedron.
The Space Diagonal of an Octahedron is the line connecting two vertices that are not on the same face of the Octahedron.
Let's assume the following value:
Using the formula:
\[ RA/V = \frac{6 \sqrt{3}}{14} \]
Evaluating:
\[ RA/V \approx 0.74230748895809 \]
The Surface to Volume Ratio is approximately 0.74230748895809 1/m.
| Space Diagonal (dSpace) (m) | Surface to Volume Ratio (RA/V) (1/m) |
|---|---|
| 10 | 1.039230484541 |
| 12 | 0.866025403784 |
| 14 | 0.742307488958 |
| 16 | 0.649519052838 |
| 18 | 0.577350269190 |