1. What is Ridge Length of Great Stellated Dodecahedron?

The Ridge Length of Great Stellated Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Stellated Dodecahedron. It's an important geometric measurement in this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_{Ridge} \) — Ridge Length of Great Stellated Dodecahedron (m)
• \( TSA \) — Total Surface Area of Great Stellated Dodecahedron (m²)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula derives from the geometric properties of the great stellated dodecahedron and the golden ratio relationship (1+√5)/2.

3. Importance of Ridge Length Calculation

Details: Calculating the ridge length is essential for understanding the proportions and structural properties of the great stellated dodecahedron, which has applications in geometry, architecture, and mathematical modeling.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a great stellated dodecahedron?
A: It's one of the Kepler-Poinsot polyhedra, created by extending the faces of a regular dodecahedron until they intersect.

Q2: Why is the golden ratio (1+√5)/2 present in the formula?
A: The golden ratio appears naturally in the geometry of regular dodecahedra and their stellated forms.

Q3: What units should I use for the calculation?
A: Use consistent units (typically meters for length and square meters for area) to ensure accurate results.

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

Q5: What if I get an unexpected result?
A: Double-check your input value and ensure it's a positive number representing the total surface area.