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The Pyramidal Height of Small Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron. It is a key geometric measurement in understanding the three-dimensional structure of this complex polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula calculates the pyramidal height based on the ridge length of the small stellated dodecahedron, incorporating the mathematical constant φ (golden ratio) through the square root of 5.
Details: Calculating the pyramidal height is essential for understanding the complete geometric properties of the small stellated dodecahedron, including its volume, surface area, and spatial relationships between its various components.
Tips: Enter the ridge length in meters. The value must be positive and greater than zero. The calculator will compute the corresponding pyramidal height.
Q1: What is a Small Stellated Dodecahedron?
A: The Small Stellated Dodecahedron is one of the Kepler-Poinsot polyhedra, formed by extending the faces of a regular dodecahedron until they meet again.
Q2: What is the relationship between ridge length and pyramidal height?
A: The pyramidal height is directly proportional to the ridge length, with the proportionality constant derived from the golden ratio and geometric properties of the shape.
Q3: Can this formula be used for other polyhedra?
A: No, this specific formula is derived for the small stellated dodecahedron and its unique geometric properties.
Q4: What are the practical applications of this calculation?
A: This calculation is primarily used in mathematical geometry, 3D modeling, and architectural design involving complex polyhedral structures.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact, provided the input ridge length is measured accurately.