The formula to calculate the Volume of an Icosahedron (\(V\)) is:
\[ V = \frac{5}{12} \times (3 + \sqrt{5}) \times \left(\frac{4 \times r_c}{\sqrt{10 + (2 \times \sqrt{5})}}\right)^3 \]
Where:
The Volume of an Icosahedron is the total quantity of three-dimensional space enclosed by the surface of the Icosahedron.
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.
Let's assume the following value:
Using the formula:
\[ V = \frac{5}{12} \times (3 + \sqrt{5}) \times \left(\frac{4 \times 9}{\sqrt{10 + (2 \times \sqrt{5})}}\right)^3 \]
Evaluating:
\[ V = 1848.85386767778 \]
The Volume is 1848.8539 m³.
| Circumsphere Radius (m) | Volume (m³) |
|---|---|
| 1 | 2.5362 |
| 2 | 20.2892 |
| 3 | 68.4761 |
| 4 | 162.3136 |
| 5 | 317.0188 |
| 6 | 547.8086 |
| 7 | 869.8997 |
| 8 | 1,298.5092 |
| 9 | 1,848.8539 |
| 10 | 2,536.1507 |