The formula to calculate the Insphere Radius of an Octahedron (\(r_i\)) is:
\[ r_i = \sqrt{\frac{2}{3}} \times r_m \]
Where:
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 Midsphere Radius of an Octahedron is the radius of the sphere for which all the edges of the Octahedron become a tangent line to that sphere.
Let's assume the following value:
Using the formula:
\[ r_i = \sqrt{\frac{2}{3}} \times r_m \]
Evaluating:
\[ r_i = \sqrt{\frac{2}{3}} \times 5 \]
The Insphere Radius is 4.0825 m.
| Midsphere Radius (m) | Insphere Radius (m) |
|---|---|
| 1 | 0.8165 |
| 2 | 1.6330 |
| 3 | 2.4495 |
| 4 | 3.2660 |
| 5 | 4.0825 |
| 6 | 4.8990 |
| 7 | 5.7155 |
| 8 | 6.5320 |
| 9 | 7.3485 |
| 10 | 8.1650 |