1. What is the Volume of Truncated Icosahedron?

The volume of a truncated icosahedron is the total three-dimensional space enclosed by its surface. A truncated icosahedron is an Archimedean solid obtained by truncating the vertices of a regular icosahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of the truncated icosahedron
• \( l_e \) — Icosahedral edge length of the truncated icosahedron
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the volume based on the edge length of the original icosahedron from which the truncated icosahedron is derived.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in various fields including mathematics, architecture, material science, and engineering for determining capacity, density, and structural properties.

4. Using the Calculator

Tips: Enter the icosahedral edge length 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 regular pentagons and 20 regular hexagons), 90 edges, and 60 vertices.

Q2: What are common applications of truncated icosahedrons?
A: The shape is famously used in soccer balls and in molecular structures such as fullerenes (buckyballs).

Q3: How accurate is this formula?
A: The formula is mathematically exact for perfect truncated icosahedrons.

Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit, but you can convert from other units before inputting the value.

Q5: What if I have the edge length of the truncated icosahedron instead?
A: This calculator specifically requires the icosahedral edge length. For truncated edge length, a different formula would be needed.