1. What is the Edge Length of Great Stellated Dodecahedron?

The edge length of a Great Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of this complex polyhedron. It is a fundamental geometric property that defines the size and scale of the shape.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( Volume \) — Total volume of the Great Stellated Dodecahedron (m³)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula derives the edge length from the volume by reversing the volume calculation formula, using the cube root relationship.

3. Importance of Edge Length Calculation

Details: Calculating the edge length from volume is essential for geometric modeling, architectural design, and understanding the spatial properties of this complex polyhedral shape.

4. Using the Calculator

Tips: Enter the volume of the Great Stellated Dodecahedron in cubic meters. The volume must be a positive value greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Stellated Dodecahedron?
A: It's a Kepler-Poinsot polyhedron that consists of 12 pentagrammic faces with three pentagrams meeting at each vertex.

Q2: Why is the golden ratio (√5) involved in the formula?
A: The Great Stellated Dodecahedron has pentagrammic faces, and the golden ratio is intrinsically related to pentagonal symmetry.

Q3: What are typical volume values for this shape?
A: Volume depends on the edge length. For example, with edge length 1m, the volume is approximately 5.0-6.0 m³.

Q4: Can this calculator handle very large or small volumes?
A: Yes, the calculator can handle a wide range of volume values, but extremely large values may cause computational limitations.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact based on the formula, with results rounded to 10 decimal places for practical use.