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Surface To Volume Ratio Of Great Icosahedron Formula:
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The Surface to Volume Ratio of a Great Icosahedron is a geometric property that represents the relationship between the total surface area and the volume of this complex polyhedron. It indicates how much surface area is available per unit volume of the shape.
The calculator uses the mathematical formula:
Where:
Explanation: This formula calculates the ratio by dividing the total surface area by the volume of the Great Icosahedron, both expressed in terms of the edge length.
Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and engineering. For polyhedra like the Great Icosahedron, this ratio helps understand properties related to surface interactions, heat transfer, and material efficiency.
Tips: Enter the edge length of the Great Icosahedron 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 Icosahedron?
A: A Great Icosahedron is a non-convex regular polyhedron and one of the Kepler-Poinsot solids. It has 20 triangular faces that intersect each other.
Q2: Why is surface to volume ratio important?
A: This ratio is important in many scientific applications including chemical reactivity, heat dissipation, biological processes, and material properties where surface area relative to volume affects behavior.
Q3: How does edge length affect the ratio?
A: The surface to volume ratio is inversely proportional to the edge length. As the size increases, the ratio decreases.
Q4: What are typical values for this ratio?
A: The ratio depends on the edge length. For smaller edge lengths, the ratio is larger, indicating relatively more surface area compared to volume.
Q5: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for the Great Icosahedron. Other polyhedra have different surface to volume ratio formulas.