The formula to calculate the Space Diagonal (dSpace) of an Octahedron given the Midsphere Radius (rm) is:
\[ d_{Space} = 2 \sqrt{2} \cdot r_{m} \]
Where:
The Space Diagonal of an Octahedron is the line connecting two vertices that are not on the same face of the Octahedron.
The Midsphere Radius of an Octahedron is the radius of the sphere for which all the edges of the Octahedron become tangent lines to that sphere.
Let's assume the following value:
Using the formula:
\[ d_{Space} = 2 \sqrt{2} \cdot 5 \]
Evaluating:
\[ d_{Space} = 2 \sqrt{2} \cdot 5 = 14.142135623731 \]
The Space Diagonal is approximately 14.142135623731 meters.
| Midsphere Radius (rm) (m) | Space Diagonal (dSpace) (m) |
|---|---|
| 5 | 14.142135623731 |
| 10 | 28.284271247462 |
| 15 | 42.426406871193 |
| 20 | 56.568542494924 |
| 25 | 70.710678118655 |