1. What is the Volume of Truncated Icosahedron?

The Volume of Truncated Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Truncated Icosahedron. It is a polyhedron with 32 faces (12 regular pentagons and 20 regular hexagons), 90 edges, and 60 vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of Truncated Icosahedron (m³)
• \( l_e \) — Edge Length of Truncated Icosahedron (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: The formula calculates the volume based on the edge length of the truncated icosahedron, incorporating the mathematical constant √5.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in mathematics, engineering, and architecture. The truncated icosahedron is particularly notable as it is the shape of a standard soccer ball.

4. Using the Calculator

Tips: Enter the edge length of the truncated icosahedron in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated icosahedron?
A: A truncated icosahedron is an Archimedean solid with 32 faces (12 pentagons and 20 hexagons), 90 edges, and 60 vertices.

Q2: Why is the formula so complex?
A: The formula incorporates the mathematical constant √5 to account for the geometric properties and symmetry of the truncated icosahedron.

Q3: What are the real-world applications of this shape?
A: The truncated icosahedron is best known as the shape of a soccer ball. It's also used in molecular structures (fullerenes) and architectural designs.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula is only applicable to truncated icosahedrons. Other polyhedra have different volume formulas.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using the formula with precise input values. The result's precision depends on the accuracy of the edge length measurement.