1. What is the 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 three-dimensional shape.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_{Ridge} \) — Ridge Length of Great Dodecahedron (m)
• \( l_e \) — Edge Length of Great Dodecahedron (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: The formula calculates the ridge length based on the edge length using the golden ratio conjugate \( \frac{\sqrt{5}-1}{2} \), which is approximately 0.618034.

3. Importance of Ridge Length Calculation

Details: Calculating the ridge length is essential for understanding the geometric properties of the Great Dodecahedron, which has applications in mathematics, architecture, and molecular structures.

4. Using the Calculator

Tips: Enter the edge length of the Great Dodecahedron in meters. The value must be positive and greater than zero.

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: Why is the golden ratio involved in this calculation?
A: The Great Dodecahedron has properties related to the golden ratio, which appears naturally in many geometric constructions.

Q3: Can this calculator be used for other polyhedra?
A: No, this specific formula applies only to the Great Dodecahedron. Other polyhedra have different geometric relationships.

Q4: What are the practical applications of this calculation?
A: This calculation is used in mathematical research, architectural design, and in understanding certain molecular structures.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, though the precision of the result depends on the precision of the input value.