Total Surface Area Of Hexakis Icosahedron Given Short Edge Calculator

Formula Used:

\[ TSA = \frac{15}{44} \times \sqrt{10 \times (417 + 107 \times \sqrt{5})} \times \left( \frac{44 \times le(Short)}{5 \times (7 - \sqrt{5})} \right)^2 \]

Total Surface Area of Hexakis Icosahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

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's an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{15}{44} \times \sqrt{10 \times (417 + 107 \times \sqrt{5})} \times \left( \frac{44 \times le(Short)}{5 \times (7 - \sqrt{5})} \right)^2 \]

Where:

\( TSA \) — Total Surface Area of Hexakis Icosahedron (m²)
\( le(Short) \) — Short Edge of Hexakis Icosahedron (m)
\( \sqrt{} \) — Square root function

Explanation: The formula calculates the total surface area based on the length of the short edge of the Hexakis Icosahedron, incorporating mathematical constants and operations.

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. It helps in determining material requirements, heat transfer calculations, and structural analysis.

4. Using the Calculator

Tips: Enter the length of the short edge in meters. The value must be positive and greater than zero. The calculator will compute the total surface area based on the provided input.

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

Q2: Why is the formula so complex?
A: The complexity comes from the irregular nature of the Hexakis Icosahedron and the mathematical relationships between its edges and surface area.

Q3: What units should I use for input?
A: The calculator uses meters as the input unit, but you can use any consistent unit system as long as you maintain consistency throughout your calculations.

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

Q5: Is this calculation accurate for real-world applications?
A: The mathematical formula provides theoretical accuracy. For real-world applications, additional factors like material properties and manufacturing tolerances should be considered.