Total Surface Area of Triakis Octahedron given Pyramidal Edge Length Calculator

Formula Used:

\[ TSA = 6 \times \left( \frac{l_{e(Pyramid)}}{2 - \sqrt{2}} \right)^2 \times \sqrt{23 - (16 \times \sqrt{2})} \]

Total Surface Area of Triakis Octahedron:

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

The Total Surface Area of Triakis Octahedron is the total quantity of plane enclosed on the entire surface of the Triakis Octahedron. It is calculated based on the pyramidal edge length using a specific mathematical formula.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 6 \times \left( \frac{l_{e(Pyramid)}}{2 - \sqrt{2}} \right)^2 \times \sqrt{23 - (16 \times \sqrt{2})} \]

Where:

\( TSA \) — Total Surface Area of Triakis Octahedron (m²)
\( l_{e(Pyramid)} \) — Pyramidal Edge Length of Triakis Octahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: The formula calculates the total surface area by converting the pyramidal edge length to the equivalent octahedral edge length and applying the surface area calculation for a Triakis Octahedron.

3. Importance of Surface Area Calculation

Details: Calculating the total surface area is important in geometry, material science, and engineering applications where the surface properties of polyhedral structures need to be determined for various calculations and analyses.

4. Using the Calculator

Tips: Enter the pyramidal edge length in meters. The value must be positive and greater than zero. The calculator will compute the total surface area using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Octahedron?
A: A Triakis Octahedron is a Catalan solid that can be seen as an octahedron with a triangular pyramid added to each face.

Q2: What units should I use for the input?
A: The pyramidal edge length should be entered in meters. The result will be in square meters.

Q3: Can this calculator handle decimal values?
A: Yes, the calculator accepts decimal values with up to 4 decimal places precision.

Q4: What is the range of valid input values?
A: The pyramidal edge length must be a positive number greater than zero.

Q5: How accurate is the calculation?
A: The calculation uses precise mathematical operations and provides results with 6 decimal places accuracy.