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 fundamental geometric property that defines the size and proportions of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• Pentagram Chord — The distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron (in meters)
• \(\sqrt{5}\) — Square root of 5 (approximately 2.23607)

Explanation: This formula establishes the precise mathematical relationship between the pentagram chord length and the edge length of the great stellated dodecahedron, utilizing the golden ratio properties inherent in pentagonal geometry.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometric properties, constructing physical models, and analyzing the spatial characteristics of the great stellated dodecahedron in mathematical and architectural applications.

4. Using the Calculator

Tips: Enter the pentagram chord length in meters. The value must be positive and valid. The calculator will automatically compute the corresponding edge length using the mathematical relationship.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Stellated Dodecahedron?
A: The Great Stellated Dodecahedron is one of the Kepler-Poinsot polyhedra, formed by extending the faces of a regular dodecahedron until they intersect, creating a star-shaped polyhedron.

Q2: What units should I use for the pentagram chord?
A: The calculator accepts meters as the unit, but you can use any consistent unit as the relationship is proportional. The result will be in the same units as your input.

Q3: Why is the golden ratio (√5) involved in this calculation?
A: The golden ratio appears naturally in pentagonal geometry, and since the great stellated dodecahedron is based on pentagonal symmetry, the golden ratio becomes an integral part of its mathematical relationships.

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

Q5: What is the typical range of values for edge length?
A: The edge length depends entirely on the size of the pentagram chord. For a given pentagram chord, the edge length will always be smaller, typically ranging from about 20-30% of the pentagram chord length.