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The Ridge Length of a Small Stellated Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the polyhedron. It's a key geometric measurement in understanding the structure of this complex shape.
The calculator uses the formula:
Where:
Explanation: The formula derives from the geometric properties of the small stellated dodecahedron and the golden ratio relationship inherent in its structure.
Details: Calculating the ridge length is essential for understanding the proportions and symmetry of the small stellated dodecahedron, which has applications in architecture, crystallography, and mathematical modeling of complex structures.
Tips: Enter the total surface area in square meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is a small stellated dodecahedron?
A: It's one of the Kepler-Poinsot polyhedra, formed by extending the faces of a regular dodecahedron until they intersect to form star-shaped points.
Q2: Why is the golden ratio (φ) present in the formula?
A: The small stellated dodecahedron exhibits five-fold symmetry and golden ratio proportions, which is why (1+√5)/2 appears in the calculation.
Q3: What are typical values for ridge length?
A: The ridge length depends entirely on the total surface area. For a standard small stellated dodecahedron with TSA of 100m², the ridge length would be approximately 7.52m.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the small 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 architectural and mathematical applications.