1. What is Surface to Volume Ratio of Truncated Icosahedron?

The Surface to Volume Ratio of a Truncated Icosahedron is a geometric measurement that compares the total surface area to the volume of this polyhedron. A truncated icosahedron is an Archimedean solid with 32 faces (12 regular pentagons and 20 regular hexagons), best known as the shape of a soccer ball.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumsphere radius of the truncated icosahedron
• \( \sqrt{} \) — Square root function

Explanation: This formula calculates the ratio of surface area to volume based on the circumsphere radius, incorporating the mathematical constants and relationships specific to the truncated icosahedron's geometry.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is important in various fields including materials science, chemistry, and physics. For truncated icosahedra (like fullerenes or buckyballs), this ratio affects properties like reactivity, dissolution rates, and thermal characteristics.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and non-zero. The calculator will compute the surface to volume ratio in reciprocal meters (m⁻¹).

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), 90 edges, and 60 vertices. It's the shape of a classic soccer ball.

Q2: What are practical applications of this calculation?
A: This calculation is useful in nanotechnology (for fullerenes), materials science, and any field dealing with particles or structures having this specific geometry.

Q3: How does circumsphere radius relate to other dimensions?
A: The circumsphere radius is the distance from the center of the truncated icosahedron to any vertex. It relates to edge length through specific mathematical relationships.

Q4: Why is surface to volume ratio important?
A: Higher surface to volume ratios typically indicate greater surface area relative to volume, which can enhance chemical reactivity, heat transfer, and other surface-dependent phenomena.

Q5: Can this calculator be used for nanoscale objects?
A: Yes, the calculation works at any scale as long as the input values are in consistent units (typically meters for SI units).