1. What is the Long Edge of Hexakis Icosahedron?

The Long Edge of Hexakis Icosahedron is the length of the longest edge that connects two opposite vertices of the Hexakis Icosahedron, a complex polyhedron with 120 triangular faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Medium Edge — Length of the medium edge of Hexakis Icosahedron (m)
• \(\sqrt{5}\) — Square root of 5 (approximately 2.23607)

Explanation: This formula establishes a precise mathematical relationship between the medium and long edges of a Hexakis Icosahedron, utilizing the golden ratio properties inherent in its geometry.

3. Importance of Long Edge Calculation

Details: Accurate calculation of the long edge is essential for geometric modeling, 3D computer graphics, architectural design, and mathematical research involving complex polyhedra.

4. Using the Calculator

Tips: Enter the medium edge length in meters. The value must be positive and non-zero. The calculator will compute the corresponding long edge length.

5. Frequently Asked Questions (FAQ)

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 the square root of 5 used in the formula?
A: The square root of 5 appears due to the golden ratio (\(\phi\)) relationships in the icosahedral symmetry, where \(\phi = \frac{1+\sqrt{5}}{2}\).

Q3: What are typical values for these edges?
A: Edge lengths vary based on the specific Hexakis Icosahedron size, but the long edge is always longer than the medium edge by the constant factor derived from the formula.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Hexakis Icosahedron due to its unique geometric properties.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, though practical accuracy depends on the precision of the input value and computational limitations.