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, which is an Archimedean solid with 12 regular pentagonal faces, 20 regular hexagonal faces, 90 edges, and 60 vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Total Surface Area — The total surface area of the truncated icosahedron (m²)

Explanation: This formula derives from the geometric properties of the truncated icosahedron, relating the edge length to the total surface area through mathematical constants and operations.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the dimensions and proportions of a truncated icosahedron, which has applications in various fields including geometry, architecture, and molecular structures (such as fullerenes in chemistry).

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero for accurate calculation.

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: Where is the truncated icosahedron found in nature?
A: The shape appears in molecular structures, particularly in fullerenes (carbon molecules), and is famously used in the design of soccer balls.

Q3: What are the units for edge length?
A: The edge length is typically measured in meters (m), consistent with the input surface area 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 surface area?
A: The formula can be rearranged to solve for total surface area given the edge length.