The formula to calculate the Insphere Radius of Icosahedron is:
\[ r_i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot l_e \]
The Insphere Radius of an Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touch the sphere. The Edge Length of an Icosahedron is the length of any of the edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron.
Let's assume the following values:
Using the formula:
\[ r_i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot 10 = 7.55761314076171 \]
The Insphere Radius of the Icosahedron is 7.55761314076171 meters.
| Edge Length (meters) | Insphere Radius (meters) |
|---|---|
| 9 | 6.801851826685536 |
| 9.5 | 7.179732483723621 |
| 10 | 7.557613140761706 |
| 10.5 | 7.935493797799792 |
| 11 | 8.313374454837877 |