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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 measurement used in three-dimensional geometry and polyhedron studies.
The calculator uses the mathematical formula:
Where:
Explanation: This formula derives the edge length from the total surface area using the geometric properties of the Great Stellated Dodecahedron, specifically its relationship with the golden ratio and pentagonal geometry.
Details: Calculating the edge length is essential for understanding the scale and proportions of the Great Stellated Dodecahedron, which has applications in mathematical modeling, architectural design, and geometric art forms.
Tips: Enter the total surface area in square meters. The value must be positive and valid. The calculator will compute the corresponding edge length of the Great Stellated Dodecahedron.
Q1: What is a Great Stellated Dodecahedron?
A: It's one of the Kepler-Poinsot polyhedra, created by extending the faces of a regular dodecahedron until they intersect, forming a star-shaped polyhedron.
Q2: Why is the formula so complex?
A: The complexity arises from the intricate geometry of the Great Stellated Dodecahedron, which involves the golden ratio (φ) and pentagonal symmetry.
Q3: What are typical values for edge length?
A: The edge length depends on the scale of the polyhedron. For a standard representation, edge lengths typically range from centimeters to meters depending on the application.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Great Stellated Dodecahedron due to its unique geometric properties.
Q5: What precision should I expect from the calculation?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most mathematical and engineering applications.