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:

• \( l_e \) — Edge Length of Truncated Icosahedron (m)
• \( r_c \) — Circumsphere Radius of Truncated Icosahedron (m)

Explanation: This formula relates the edge length of a truncated icosahedron to the radius of its circumscribed sphere through a mathematical constant derived from the geometry of the solid.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometric properties 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 circumsphere radius in meters. The value must be positive and non-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 this shape commonly found?
A: The truncated icosahedron is best known as the shape of a soccer ball and the molecular structure of buckminsterfullerene (C₆₀).

Q3: What are the units for this calculation?
A: Both the circumsphere radius and edge length are typically measured in meters, though any consistent unit system can be used.

Q4: How accurate is this formula?
A: This formula is mathematically exact for perfect truncated icosahedrons and provides precise calculations.

Q5: Can this calculator handle different units?
A: The calculator uses the same units for input and output. For different units, convert your measurements accordingly before calculation.