The formula to calculate the Circumsphere Radius of Icosahedron is:
\[ r_c = \frac{\sqrt{10 + 2\sqrt{5}}}{4} \cdot l_e \]
The Circumsphere Radius of an Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on 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:
\[ r_c = \frac{\sqrt{10 + 2\sqrt{5}}}{4} \cdot 10 = 9.51056516295153 \]
The Circumsphere Radius of the Icosahedron is 9.51056516295153 meters.
| Edge Length (meters) | Circumsphere Radius (meters) |
|---|---|
| 9 | 8.559508646656381 |
| 9.5 | 9.035036904803958 |
| 10 | 9.510565162951535 |
| 10.5 | 9.986093421099111 |
| 11 | 10.461621679246688 |