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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 measurement in this complex polyhedron.
The calculator uses the mathematical formula:
Where:
Explanation: This formula establishes the precise mathematical relationship between the ridge length and edge length in a Great Stellated Dodecahedron, incorporating the golden ratio through the square root of 5.
Details: Accurate calculation of edge length is crucial for geometric modeling, architectural design, and mathematical analysis of the Great Stellated Dodecahedron's properties and proportions.
Tips: Enter the ridge length in meters. The value must be positive and valid. The calculator will automatically compute the corresponding edge length using the mathematical relationship.
Q1: What is a Great Stellated Dodecahedron?
A: The Great Stellated Dodecahedron is one of the Kepler-Poinsot polyhedra, featuring star-shaped faces and complex geometric properties.
Q2: Why does the formula include √5?
A: The square root of 5 appears because it relates to the golden ratio (φ), which is fundamental to the geometry of dodecahedrons and their stellations.
Q3: What are typical values for ridge length?
A: Ridge length values depend on the specific size of the polyhedron being measured, but they are always positive real numbers.
Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit, but you can use any consistent unit system as long as both input and output use the same units.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact, providing precise results based on the geometric properties of the Great Stellated Dodecahedron.