Edge Length of Truncated Icosahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ l_e = \frac{12 \times (10\sqrt{3} + \sqrt{25 + 10\sqrt{5}})}{R_{A/V} \times (125 + 43\sqrt{5})} \]

Edge Length (l_e):

Unit Converter ▲

Unit Converter ▼

From:	To:

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 32 faces (12 regular pentagons and 20 regular hexagons).

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_e = \frac{12 \times (10\sqrt{3} + \sqrt{25 + 10\sqrt{5}})}{R_{A/V} \times (125 + 43\sqrt{5})} \]

Where:

\( l_e \) — Edge length of truncated icosahedron (m)
\( R_{A/V} \) — Surface to volume ratio (1/m)
\( \sqrt{3} \) — Square root of 3 (≈1.732)
\( \sqrt{5} \) — Square root of 5 (≈2.236)

Explanation: This formula calculates the edge length of a truncated icosahedron based on its surface to volume ratio, incorporating the mathematical constants and geometric properties specific to this polyhedron.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometric properties, volume, surface area, and other characteristics of truncated icosahedrons, which have applications in various fields including chemistry, architecture, and materials science.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. 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 with 32 faces (12 pentagons and 20 hexagons), best known as the shape of a soccer ball.

Q2: Why is this calculation important?
A: This calculation helps in determining the physical dimensions of truncated icosahedral structures, which is crucial in various scientific and engineering applications.

Q3: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the specific application and scale, but generally ranges from very small to very large values depending on the size of the polyhedron.

Q4: Are there limitations to this formula?
A: This formula is mathematically exact for perfect truncated icosahedrons. Real-world applications may require adjustments for manufacturing tolerances or material properties.

Q5: Can this calculator be used for other polyhedrons?
A: No, this calculator is specifically designed for truncated icosahedrons. Other polyhedrons have different formulas for edge length calculation.