Total Surface Area of Hexakis Icosahedron Calculator

Total Surface Area of Hexakis Icosahedron Formula:

\[ TSA = \frac{15}{44} \times \sqrt{10 \times (417 + 107 \times \sqrt{5})} \times (Long Edge)^2 \]

Total Surface Area of Hexakis Icosahedron:

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1. What is the Total Surface Area of Hexakis Icosahedron?

The Total Surface Area of Hexakis Icosahedron is the amount or quantity of two dimensional space covered by the surface of Hexakis Icosahedron. It is an important geometric measurement used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{15}{44} \times \sqrt{10 \times (417 + 107 \times \sqrt{5})} \times (Long Edge)^2 \]

Where:

\( TSA \) — Total Surface Area of Hexakis Icosahedron (m²)
\( Long Edge \) — Length of the longest edge of Hexakis Icosahedron (m)

Explanation: This formula calculates the total surface area based on the long edge measurement of the Hexakis Icosahedron, incorporating mathematical constants and square root functions.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of geometric shapes is crucial in various fields including architecture, engineering, material science, and 3D modeling for determining material requirements, heat transfer calculations, and structural analysis.

4. Using the Calculator

Tips: Enter the long edge measurement in meters. The value must be positive and greater than zero. The calculator will compute the total surface area in square meters.

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 icosahedron. It has 120 faces, 180 edges, and 62 vertices.

Q2: Why is the formula so complex?
A: The formula incorporates mathematical constants and square root functions to accurately calculate the surface area of this complex polyhedron based on its geometric properties.

Q3: What units should I use for input?
A: Input the long edge measurement in meters. The result will be in square meters. You can convert from other units as needed before input.

Q4: Can this calculator handle very large or small values?
A: The calculator can handle a wide range of values, but extremely large or small numbers may be limited by PHP's floating point precision.

Q5: Is this calculation accurate for real-world applications?
A: This provides a mathematical calculation of surface area. For real-world applications, additional factors such as material thickness, manufacturing tolerances, and surface imperfections may need to be considered.