Total Surface Area Of Triakis Icosahedron Calculator

Total Surface Area of Triakis Icosahedron Formula:

\[ TSA = \frac{15}{11} \times \sqrt{109 - 30\sqrt{5}} \times (le(Icosahedron))^2 \]

Total Surface Area (TSA):

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

The Total Surface Area of Triakis Icosahedron is the amount or quantity of two dimensional space covered on the surface of Triakis Icosahedron. It represents the sum of the areas of all the faces of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{15}{11} \times \sqrt{109 - 30\sqrt{5}} \times (le(Icosahedron))^2 \]

Where:

\( TSA \) — Total Surface Area of Triakis Icosahedron (m²)
\( le(Icosahedron) \) — Icosahedral Edge Length of Triakis Icosahedron (m)

Explanation: The formula calculates the total surface area based on the icosahedral edge length, incorporating mathematical constants and square root functions.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of polyhedra is important in geometry, material science, and various engineering applications where surface properties need to be determined.

4. Using the Calculator

Tips: Enter the icosahedral edge length in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Icosahedron?
A: A Triakis Icosahedron is a Catalan solid that is the dual of the truncated dodecahedron. It has 60 faces, each being an isosceles triangle.

Q2: What units should I use for the input?
A: The calculator uses meters for length input, but you can use any consistent unit as long as you maintain the same unit for all measurements.

Q3: How accurate is the calculation?
A: The calculation uses precise mathematical constants and provides results with 6 decimal places for accuracy.

Q4: Can this calculator handle very large or very small values?
A: The calculator can handle a wide range of positive values, though extremely large values may cause computational limitations.

Q5: What are some practical applications of this calculation?
A: Surface area calculations are used in material science, architecture, 3D modeling, and various engineering disciplines where surface properties are important.