The formula to calculate the insphere radius of an octahedron given its space diagonal is:
\[ \text{Insphere Radius} = \frac{\text{Space Diagonal}}{2 \cdot \sqrt{3}} \]
The insphere radius of an octahedron is the radius of the sphere that is contained by the octahedron in such a way that all the faces are just touching the sphere.
Let's assume the following value:
Using the formula:
\[ \text{Insphere Radius} = \frac{14}{2 \cdot \sqrt{3}} \approx 4.0415 \, \text{meters} \]
The insphere radius is approximately 4.0415 meters.
| Space Diagonal (meters) | Insphere Radius (meters) |
|---|---|
| 14 | 4.0415 |
| 20 | 5.7735 |
| 25 | 7.2169 |