The formula to calculate the Insphere Radius of Icosahedron is:
\[ ri = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{TSA}{5 \cdot \sqrt{3}}} \]
Insphere Radius of 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. Total Surface Area of Icosahedron is the total quantity of plane enclosed by the entire surface of the Icosahedron.
Let's assume the following values:
Using the formula:
\[ ri = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{870}{5 \cdot \sqrt{3}}} = 7.57493600114069 \]
The Insphere Radius is 7.57493600114069 Meters.
| Total Surface Area (Square Meters) | Insphere Radius (Meters) |
|---|---|
| 850 | 7.487361543491459 |
| 860 | 7.531276063999118 |
| 870 | 7.574936001140687 |
| 880 | 7.618345731888814 |
| 890 | 7.661509509215514 |