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:

• \( Midsphere\ Radius \) — Radius of the midsphere (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula relates the edge length of a truncated icosahedron to the radius of its midsphere, which is the sphere tangent to all its edges.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometry of truncated icosahedrons, which have applications in various fields including architecture, chemistry (fullerenes), and sports equipment design (soccer balls).

4. Using the Calculator

Tips: Enter the midsphere radius in 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: What is the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q3: Are there other ways to calculate edge length?
A: Yes, the edge length can also be calculated using other parameters such as volume, surface area, or circumsphere radius using different formulas.

Q4: What are typical applications of truncated icosahedrons?
A: Truncated icosahedrons are famously used in the design of soccer balls and appear in molecular structures of fullerenes (Buckminsterfullerene, C60).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using the precise formula, though practical measurements may introduce some error.