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Volume Of Great Stellated Dodecahedron Formula:
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The Volume Of Great Stellated Dodecahedron represents the total three-dimensional space enclosed by the surface of this complex polyhedron. It is one of the Kepler-Poinsot solids, known for its star-like appearance with pentagrammic faces.
The calculator uses the mathematical formula:
Where:
Explanation: This formula calculates the volume based on the edge length, incorporating the mathematical constant related to the golden ratio.
Details: Calculating the volume of geometric solids is fundamental in mathematics, architecture, and engineering. For the Great Stellated Dodecahedron, this calculation helps in understanding its spatial properties and applications in various fields including crystallography and artistic design.
Tips: Enter the edge length in meters. The value must be positive and non-zero. The calculator will compute the volume using the precise mathematical formula.
Q1: What is a Great Stellated Dodecahedron?
A: It is one of the four Kepler-Poinsot solids, formed by extending the faces of a regular dodecahedron until they intersect, creating a star-shaped polyhedron.
Q2: What units should I use for edge length?
A: The calculator uses meters, but you can use any unit as long as you're consistent (the volume will be in cubic units of your input).
Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Great Stellated Dodecahedron. Other polyhedra have different volume formulas.
Q4: What is the significance of √5 in the formula?
A: The square root of 5 appears in many mathematical contexts involving the golden ratio, which is fundamental to the geometry of pentagonal shapes.
Q5: How accurate is the calculation?
A: The calculation is mathematically precise based on the input edge length, using the exact formula for this specific polyhedron.