Total Surface Area Of Hexakis Octahedron Given Medium Edge Calculator

Formula Used:

\[ TSA = \frac{3}{7} \times \sqrt{543 + 176\sqrt{2}} \times \left( \frac{14 \times le(Medium)}{3 \times (1 + 2\sqrt{2})} \right)^2 \]

Total Surface Area of Hexakis Octahedron:

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

The Total Surface Area of a Hexakis Octahedron is the total area of all the faces of this polyhedron. It's an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{3}{7} \times \sqrt{543 + 176\sqrt{2}} \times \left( \frac{14 \times le(Medium)}{3 \times (1 + 2\sqrt{2})} \right)^2 \]

Where:

\( TSA \) — Total Surface Area of Hexakis Octahedron (m²)
\( le(Medium) \) — Medium Edge of Hexakis Octahedron (m)

Explanation: This formula calculates the total surface area based on the medium edge length of the Hexakis Octahedron, incorporating mathematical constants and square roots.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is crucial for various applications including material estimation, structural analysis, and geometric modeling of complex polyhedra.

4. Using the Calculator

Tips: Enter the medium edge length in meters. The value must be positive and valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Hexakis Octahedron?
A: A Hexakis Octahedron is a Catalan solid that is the dual of the truncated cuboctahedron, featuring 48 faces, 72 edges, and 26 vertices.

Q2: What are the different edge lengths in a Hexakis Octahedron?
A: A Hexakis Octahedron has three types of edges: short, medium, and long edges, with the medium edge being used in this calculation.

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

Q4: How accurate is this calculation?
A: The calculation is mathematically precise based on the geometric properties of the Hexakis Octahedron, provided accurate input values are given.

Q5: Can this formula be used for other polyhedra?
A: No, this specific formula is designed only for calculating the total surface area of a Hexakis Octahedron given its medium edge length.