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The Pyramidal Height of Great Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Stellated Dodecahedron. It represents the distance from the center of the base pyramid to its apex.
The calculator uses the formula:
Where:
Explanation: This formula provides a direct relationship between the circumradius and the pyramidal height of the Great Stellated Dodecahedron, where the pyramidal height is exactly two-thirds of the circumradius.
Details: Calculating the pyramidal height is essential for understanding the geometric properties and spatial dimensions of the Great Stellated Dodecahedron. It helps in various mathematical and engineering applications involving this complex polyhedron.
Tips: Enter the circumradius value in meters. The value must be positive and greater than zero to compute a valid pyramidal height.
Q1: What is the Great Stellated Dodecahedron?
A: The Great Stellated Dodecahedron is one of the Kepler-Poinsot polyhedra, formed by extending the faces of a regular dodecahedron until they intersect.
Q2: How is circumradius related to pyramidal height?
A: The pyramidal height is exactly two-thirds of the circumradius in a Great Stellated Dodecahedron, as given by the formula h = 2r/3.
Q3: What units should be used for input?
A: The calculator accepts input in meters, but any consistent unit of length can be used as long as both input and output use the same unit.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Great Stellated Dodecahedron. Other polyhedra have different geometric relationships.
Q5: What is the practical application of this calculation?
A: This calculation is primarily used in mathematical geometry, 3D modeling, and architectural design involving complex polyhedral structures.