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 faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Total Surface Area — The total surface area of the Hexakis Icosahedron (m²)

Explanation: This formula calculates the longest edge length based on the total surface area of the polyhedron, using mathematical constants specific to its geometry.

3. Importance of Long Edge Calculation

Details: Calculating the long edge is essential for understanding the dimensions and proportions of Hexakis Icosahedron in geometric modeling, architectural design, and mathematical research.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero.

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 triangular faces.

Q2: Why is this specific formula used?
A: The formula is derived from the geometric properties and mathematical relationships specific to the Hexakis Icosahedron's structure.

Q3: What are typical values for the long edge?
A: The long edge length varies depending on the total surface area, but typically ranges from a few centimeters to several meters in practical applications.

Q4: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for the Hexakis Icosahedron and uses formulas unique to its geometry.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise when correct input values are provided, with results rounded to six decimal places for clarity.