The formula to calculate the Volume of an Icosahedron is:
\[ \text{Volume of Icosahedron} = \frac{5}{12} (3 + \sqrt{5}) \times le^3 \]
Where:
Volume of Icosahedron is the total quantity of three-dimensional space enclosed by the surface of the Icosahedron.
Let's assume the following value:
Using the formula:
\[ \text{Volume of Icosahedron} = \frac{5}{12} (3 + \sqrt{5}) \times 10^3 \]
Evaluating:
\[ \text{Volume of Icosahedron} = \frac{5}{12} (3 + \sqrt{5}) \times 1000 \]
\[ \text{Volume of Icosahedron} = \frac{5}{12} \times 5.23606797749979 \times 1000 \]
\[ \text{Volume of Icosahedron} = 2181.69499062491 \]
The Volume of the Icosahedron is approximately 2181.69499062491 cubic meters.
| Edge Length of Icosahedron (meters) | Volume of Icosahedron (cubic meters) |
|---|---|
| 1 | 2.181694990625 |
| 2 | 17.453559924999 |
| 3 | 58.905764746873 |
| 4 | 139.628479399994 |
| 5 | 272.711873828114 |
| 6 | 471.246117974981 |
| 7 | 748.321381784345 |
| 8 | 1,117.027835199955 |
| 9 | 1,590.455648165561 |
| 10 | 2,181.694990624912 |
| 11 | 2,903.836032521759 |
| 12 | 3,769.968943799849 |
| 13 | 4,793.183894402933 |
| 14 | 5,986.571054274760 |
| 15 | 7,363.220593359080 |
| 16 | 8,936.222681599642 |
| 17 | 10,718.667488940195 |
| 18 | 12,723.645185324491 |
| 19 | 14,964.245940696275 |
| 20 | 17,453.559924999299 |