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Surface To Volume Ratio Of Great Dodecahedron Formula:
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The Surface to Volume Ratio of a Great Dodecahedron is a geometric measurement that compares the total surface area of the polyhedron to its volume. This ratio is important in various mathematical and engineering applications where surface properties relative to volume are significant.
The calculator uses the formula:
Where:
Explanation: The formula calculates how much surface area exists per unit volume of the Great Dodecahedron, which is a Kepler-Poinsot polyhedron with pentagrammic faces.
Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and physics. For polyhedra, this ratio helps understand properties like heat transfer, diffusion rates, and structural efficiency.
Tips: Enter the edge length of the Great Dodecahedron in meters. The value must be positive and greater than zero. The calculator will compute the surface to volume ratio in reciprocal meters (m⁻¹).
Q1: What is a Great Dodecahedron?
A: A Great Dodecahedron is one of the four Kepler-Poinsot polyhedra, consisting of 12 pentagrammic faces that intersect each other.
Q2: Why is surface to volume ratio important?
A: This ratio is critical in processes where surface interactions are important, such as chemical reactions, heat transfer, and fluid dynamics.
Q3: How does edge length affect the ratio?
A: As edge length increases, the surface to volume ratio decreases, following the inverse relationship typical for geometric shapes.
Q4: What are typical values for this ratio?
A: The ratio depends entirely on the edge length. For a Great Dodecahedron with 1m edge length, the ratio is approximately 0.7053 m⁻¹.
Q5: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for the Great Dodecahedron. Other polyhedra have different surface to volume ratio formulas.