The formula to calculate the Insphere Radius of an Octahedron given its circumsphere radius is:
\[ \text{Insphere Radius} = \frac{\text{Circumsphere Radius}}{\sqrt{3}} \]
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. The Circumsphere Radius of an Octahedron is the radius of the sphere that contains the octahedron in such a way that all the vertices are lying on the sphere.
Let's assume the following value:
Using the formula:
\[ \text{Insphere Radius} = \frac{7}{\sqrt{3}} \approx 4.0415 \, \text{meters} \]
The Insphere Radius is approximately 4.0415 meters.
| Circumsphere Radius (meters) | Insphere Radius (meters) |
|---|---|
| 6 | 3.464101615137755 |
| 6.5 | 3.752776749732567 |
| 7 | 4.041451884327381 |
| 7.5 | 4.330127018922194 |
| 8 | 4.618802153517007 |