Formula Used:
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The Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron. It is a key geometric measurement that helps in understanding the three-dimensional structure and properties of this complex polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula calculates the pyramidal height based on the circumsphere radius, incorporating mathematical constants and geometric relationships specific to the Great Dodecahedron.
Details: Calculating the pyramidal height is essential for understanding the internal structure of the Great Dodecahedron, its volume properties, and its geometric relationships with other polyhedral measurements.
Tips: Enter the circumsphere radius in meters. The value must be positive and non-zero. The calculator will compute the corresponding pyramidal height using the mathematical formula.
Q1: What is a Great Dodecahedron?
A: The Great Dodecahedron is one of the Kepler-Poinsot polyhedra, consisting of 12 pentagonal faces that intersect each other, creating a complex star-shaped polyhedron.
Q2: What is the circumsphere radius?
A: The circumsphere radius is the radius of the sphere that contains the Great Dodecahedron such that all vertices lie on the sphere's surface.
Q3: How accurate is this calculation?
A: The calculation is mathematically precise based on the given formula, with results rounded to 12 decimal places for practical use.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Great Dodecahedron due to its unique geometric properties.
Q5: What are typical values for pyramidal height?
A: The pyramidal height varies with the size of the polyhedron but maintains a constant proportional relationship with the circumsphere radius.