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The Long Edge of Hexakis Icosahedron is the length of the longest edge that connects two opposite vertices of the Hexakis Icosahedron. It is a key geometric parameter in understanding the dimensions and properties of this complex polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula calculates the long edge length based on the volume of the Hexakis Icosahedron, using mathematical constants and operations including square roots and cube roots.
Details: Calculating the long edge is essential for understanding the geometric properties, spatial dimensions, and structural characteristics of Hexakis Icosahedrons in mathematical modeling and engineering applications.
Tips: Enter the volume of the Hexakis Icosahedron in cubic meters. The value must be positive and valid for accurate calculation.
Q1: What is a Hexakis Icosahedron?
A: A Hexakis Icosahedron is a Catalan solid that is the dual of the truncated dodecahedron, featuring 120 faces, 180 edges, and 62 vertices.
Q2: Why is this specific formula used?
A: This formula is derived from the geometric relationships between volume and edge lengths in Hexakis Icosahedrons, incorporating mathematical constants specific to this polyhedron.
Q3: What are typical volume values for Hexakis Icosahedrons?
A: Volume values vary significantly based on the size of the polyhedron, ranging from very small (fractional cubic meters) to large values depending on the application.
Q4: Can this calculator be used for other polyhedrons?
A: No, this calculator is specifically designed for Hexakis Icosahedrons. Other polyhedrons have different geometric relationships and require different formulas.
Q5: How accurate are the results?
A: The results are mathematically precise based on the input volume, with accuracy limited only by computational precision and the accuracy of the input value.