1. What is Ridge Length of Great Dodecahedron?

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

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

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

3. Formula Explanation

Mathematical Basis: This formula derives from the geometric properties of the Great Dodecahedron, specifically the relationship between its total surface area and the ridge length. The constants involve the golden ratio and square roots that are characteristic of dodecahedral geometry.

4. Using the Calculator

Instructions: Enter the total surface area of the Great Dodecahedron in square meters. The value must be positive and greater than zero. Click calculate to get the ridge length result.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Dodecahedron?
A: The Great Dodecahedron is one of the Kepler-Poinsot polyhedra, consisting of 12 pentagonal faces that intersect each other.

Q2: What units should I use for input?
A: The calculator expects total surface area in square meters (m²) and returns ridge length in meters (m).

Q3: Can this formula be used for any dodecahedron?
A: No, this specific formula applies only to the Great Dodecahedron, not regular dodecahedrons or other variants.

Q4: What is the typical range of values?
A: The ridge length depends on the size of the polyhedron. For standard mathematical models, values typically range from centimeters to meters scale.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the Great Dodecahedron, limited only by computational precision.