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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 key geometric parameter that defines the size and proportions of this complex polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula establishes the mathematical relationship between the pyramidal height and the edge length of the Great Stellated Dodecahedron, incorporating fundamental mathematical constants.
Details: Accurate calculation of edge length is essential for geometric modeling, architectural design, and mathematical analysis of the Great Stellated Dodecahedron's properties and proportions.
Tips: Enter the pyramidal height in meters. The value must be positive and valid for accurate calculation of the edge length.
Q1: What is the Great Stellated Dodecahedron?
A: The Great Stellated Dodecahedron is one of the Kepler-Poinsot polyhedra, featuring star-shaped faces and complex geometric properties.
Q2: How is pyramidal height defined for this polyhedron?
A: Pyramidal height refers to the height of any of the inwards directed tetrahedral pyramids of the Great Stellated Dodecahedron.
Q3: What are typical values for edge length in practical applications?
A: Edge length values vary depending on the scale of the polyhedron, ranging from millimeters in models to meters in architectural applications.
Q4: Are there limitations to this calculation?
A: This formula assumes a perfect geometric construction and may need adjustment for physical implementations with material thickness.
Q5: 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.