1. What is the Edge Length of Truncated Icosahedron?

The Edge Length of Truncated Icosahedron is the length of any edge of the Truncated Icosahedron, which is an Archimedean solid formed by truncating the corners of a regular icosahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge Length of Truncated Icosahedron (m)
• \( l_{e(Icosahedron)} \) — Icosahedral Edge Length of Truncated Icosahedron (m)

Explanation: The formula shows that the edge length of the truncated icosahedron is exactly one-third of the edge length of the original icosahedron from which it is derived.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for determining various geometric properties of the truncated icosahedron, including surface area, volume, and other dimensional characteristics.

4. Using the Calculator

Tips: Enter the icosahedral edge length in 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 with 12 regular pentagonal faces, 20 regular hexagonal faces, 90 edges, and 60 vertices.

Q2: Why is the edge length exactly one-third of the original?
A: This relationship comes from the specific truncation process where the corners of the original icosahedron are cut off at exactly one-third of the edge length from each vertex.

Q3: What are the applications of truncated icosahedron?
A: The truncated icosahedron is best known as the shape of a soccer ball and is also used in various architectural and molecular structures.

Q4: Can this formula be used for other truncated polyhedra?
A: No, this specific formula applies only to the truncated icosahedron. Different polyhedra have different truncation ratios.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when the input values are precise, as it's based on a simple geometric ratio.