1. What is the Edge Length of Truncated Icosahedron?

The edge length of a truncated icosahedron is the length of any edge of this polyhedron. A truncated icosahedron is an Archimedean solid 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:

• \( Volume \) — Volume of the truncated icosahedron (m³)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula derives from the geometric properties of the truncated icosahedron and allows calculation of edge length when the volume is known.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for various applications in geometry, material science, and architecture where the truncated icosahedron shape is used, such as in soccer balls and fullerene molecules.

4. Using the Calculator

Tips: Enter the volume of the truncated icosahedron in cubic meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated icosahedron?
A: A truncated icosahedron is an Archimedean solid obtained by truncating the vertices of a regular icosahedron, resulting in 12 pentagonal and 20 hexagonal faces.

Q2: Why is this shape significant?
A: This shape is famous for its appearance in soccer balls and carbon fullerene molecules (C60 buckyballs).

Q3: What are the units for edge length?
A: The edge length is calculated in meters (m), matching the volume input units.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to truncated icosahedrons due to their unique geometric properties.

Q5: What if I have the edge length and want to find the volume?
A: The formula can be rearranged to calculate volume from edge length: \( Volume = \frac{Edge\ Length^3 \times (125 + 43\sqrt{5})}{4} \)