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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 an important geometric measurement in this polyhedral shape.
The calculator uses the formula:
Where:
Explanation: This formula provides a precise mathematical relationship between the short and long edges of a Hexakis Icosahedron based on its geometric properties.
Details: Calculating the long edge is essential for understanding the complete geometry of the Hexakis Icosahedron, which has applications in various fields including crystallography, architecture, and mathematical modeling.
Tips: Enter the short edge length in meters. The value must be positive and valid. The calculator will compute the corresponding long edge length.
Q1: What is a Hexakis Icosahedron?
A: A Hexakis Icosahedron is a Catalan solid that is the dual of the truncated dodecahedron. It has 120 faces, 180 edges, and 62 vertices.
Q2: Why is there a square root in the formula?
A: The square root of 5 appears in the formula due to the golden ratio relationship that is fundamental to the geometry of icosahedral shapes.
Q3: Can this formula be used for any Hexakis Icosahedron?
A: Yes, this formula applies to all regular Hexakis Icosahedrons where the ratio between edges remains constant.
Q4: What are practical applications of this calculation?
A: This calculation is useful in geometric modeling, 3D design, architectural structures, and mathematical research involving polyhedral shapes.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using the precise formula. The result accuracy depends on the precision of the input value and the computational precision of the calculator.