1. What is Circumsphere Radius of Great Dodecahedron?

The Circumsphere Radius of a Great Dodecahedron is the radius of the sphere that contains the polyhedron such that all vertices lie on the sphere's surface. It is a fundamental geometric property of this particular polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumsphere Radius (m)
• \( \frac{A}{V} \) — Surface to Volume Ratio (m⁻¹)

Explanation: This formula calculates the circumsphere radius based on the surface to volume ratio of the Great Dodecahedron, incorporating mathematical constants related to its geometric properties.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important for understanding the spatial dimensions and geometric properties of the Great Dodecahedron, which has applications in various fields including crystallography, architecture, and mathematical modeling.

4. Using the Calculator

Tips: Enter the surface to volume ratio in m⁻¹. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Dodecahedron?
A: A Great Dodecahedron is a Kepler-Poinsot polyhedron with 12 pentagonal faces that intersect each other.

Q2: How is surface to volume ratio defined?
A: Surface to volume ratio is the total surface area divided by the volume of the polyhedron, measured in m⁻¹.

Q3: What are typical values for circumsphere radius?
A: The circumsphere radius depends on the specific dimensions of the Great Dodecahedron and can vary significantly based on its size.

Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for the Great Dodecahedron polyhedron.

Q5: What precision should I expect from the calculation?
A: The calculator provides results with 6 decimal places precision, which is suitable for most geometric calculations.