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

The Surface to Volume Ratio of a Great Icosahedron is a geometric property that represents the relationship between the total surface area and the volume of this complex polyhedron. It's an important parameter in materials science and geometry studies.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumsphere Radius of the Great Icosahedron (m)
• \( \sqrt{} \) — Square root function

Explanation: This formula calculates the surface area to volume ratio based on the circumsphere radius, incorporating the geometric constants specific to the Great Icosahedron's structure.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various applications including material science, chemical reactivity studies, heat transfer analysis, and understanding geometric properties of complex polyhedra.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Icosahedron?
A: A Great Icosahedron is a non-convex regular polyhedron and one of the Kepler-Poinsot solids, featuring intersecting triangular faces.

Q2: Why is surface to volume ratio important?
A: It indicates how much surface area is available per unit volume, which affects properties like reactivity, heat dissipation, and structural efficiency.

Q3: What units are used in this calculation?
A: The circumsphere radius is in meters (m), and the surface to volume ratio is in reciprocal meters (m⁻¹).

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Great Icosahedron due to its unique geometric properties.

Q5: What is the typical range of values?
A: The surface to volume ratio decreases as the size (circumsphere radius) increases, following an inverse relationship.