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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's an important parameter in various mathematical and engineering applications.
The calculator uses the following formula:
Where:
Explanation: This formula calculates the surface area to volume ratio based on the geometric properties of the Great Icosahedron and its long ridge length measurement.
Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and engineering. For complex polyhedra like the Great Icosahedron, this ratio helps understand properties related to surface interactions, heat transfer, and structural efficiency.
Tips: Enter the long ridge length of the Great Icosahedron in meters. The value must be positive and greater than zero. The calculator will compute the corresponding surface to volume ratio.
Q1: What is a Great Icosahedron?
A: The Great Icosahedron is one of the four regular star polyhedra, also known as the Kepler-Poinsot polyhedra. It has 20 triangular faces that intersect each other.
Q2: What are the typical values for surface to volume ratio?
A: The surface to volume ratio depends on the long ridge length. Smaller lengths result in higher ratios, while larger lengths result in lower ratios.
Q3: What units are used in this calculation?
A: The long ridge length is input in meters (m), and the surface to volume ratio is output in reciprocal meters (m⁻¹).
Q4: Can this calculator handle very small or very large values?
A: Yes, the calculator can handle a wide range of positive values, though extremely small values may approach computational limits.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the Great Icosahedron, with precision limited only by computational floating-point arithmetic.