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 is a key geometric parameter in understanding the structure of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_{Ridge} \) — Ridge Length of Great Dodecahedron (m)
• \( r_c \) — Circumsphere Radius of Great Dodecahedron (m)

Explanation: This formula calculates the ridge length based on the circumsphere radius, using the golden ratio and geometric properties of the great dodecahedron.

3. Importance of Ridge Length Calculation

Details: Calculating the ridge length is essential for understanding the geometric properties of the great dodecahedron, its symmetry, and for applications in architecture, crystallography, and mathematical modeling.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and valid.

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 is the significance of the golden ratio in this formula?
A: The golden ratio (φ = (√5+1)/2) appears frequently in the geometry of regular polyhedra, including the great dodecahedron.

Q3: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect great dodecahedron with the given circumsphere radius.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the great dodecahedron. Other polyhedra have different geometric relationships.

Q5: What are practical applications of this calculation?
A: Applications include architectural design, molecular modeling, computer graphics, and mathematical education.