The formula to calculate the Insphere Radius of Dodecahedron is:
\[ ri = \sqrt{\frac{25 + 11\sqrt{5}}{10}} \cdot \frac{le}{2} \]
Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touch the sphere. Edge Length of Dodecahedron is the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron.
Let's assume the following values:
Using the formula:
\[ ri = \sqrt{\frac{25 + 11\sqrt{5}}{10}} \cdot \frac{10}{2} = 11.1351636441161 \]
The Insphere Radius is 11.1351636441161 Meters.
| Edge Length (Meters) | Insphere Radius (Meters) |
|---|---|
| 9 | 10.021647279704462 |
| 9.5 | 10.578405461910265 |
| 10 | 11.135163644116069 |
| 10.5 | 11.691921826321872 |
| 11 | 12.248680008527675 |