Edge Length of Great Stellated Dodecahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ le = \frac{15 \times \sqrt{5 + (2 \times \sqrt{5})}}{\frac{5}{4} \times (3 + \sqrt{5}) \times AV} \]

Edge Length of Great Stellated Dodecahedron:

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1. What is the Edge Length of Great Stellated Dodecahedron?

The Edge Length of Great Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Stellated Dodecahedron. It is a key geometric parameter in understanding the structure and properties of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ le = \frac{15 \times \sqrt{5 + (2 \times \sqrt{5})}}{\frac{5}{4} \times (3 + \sqrt{5}) \times AV} \]

Where:

\( le \) — Edge Length of Great Stellated Dodecahedron (m)
\( AV \) — SA:V of Great Stellated Dodecahedron (1/m)

Explanation: This formula calculates the edge length based on the surface area to volume ratio of the Great Stellated Dodecahedron.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometric properties, scaling, and spatial characteristics of the Great Stellated Dodecahedron in mathematical and architectural applications.

4. Using the Calculator

Tips: Enter the SA:V of Great Stellated Dodecahedron in 1/m. The value must be greater than 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Stellated Dodecahedron?
A: The Great Stellated Dodecahedron is a Kepler-Poinsot polyhedron with star-shaped faces, formed by extending the faces of a regular dodecahedron.

Q2: How is SA:V ratio defined?
A: SA:V (Surface Area to Volume Ratio) is the ratio of the total surface area to the volume of a three-dimensional object.

Q3: What are typical values for SA:V ratio?
A: The SA:V ratio varies depending on the size and shape of the polyhedron. Smaller objects typically have higher SA:V ratios.

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

Q5: What units should I use?
A: Use consistent units - meters for length and 1/m for SA:V ratio.