Total Surface Area Of Hexakis Octahedron Given Truncated Cuboctahedron Edge Calculator

Formula Used:

\[ TSA = \frac{3}{7} \times \frac{4}{49} \times \sqrt{543 + 176\sqrt{2}} \times (60 + 6\sqrt{2}) \times (l_e)^2 \]

Total Surface Area (TSA):

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

The Total Surface Area (TSA) of a Hexakis Octahedron is the total area of all its faces. It is a measure of the extent of the surface that the polyhedron covers.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{3}{7} \times \frac{4}{49} \times \sqrt{543 + 176\sqrt{2}} \times (60 + 6\sqrt{2}) \times (l_e)^2 \]

Where:

\( TSA \) — Total Surface Area of Hexakis Octahedron (m²)
\( l_e \) — Truncated Cuboctahedron Edge length (m)

Explanation: The formula accounts for the geometric properties of the Hexakis Octahedron derived from truncating a Cuboctahedron.

3. Importance of TSA Calculation

Details: Calculating the total surface area is essential in various fields such as material science, architecture, and 3D modeling for determining properties like coverage, material requirements, and structural analysis.

4. Using the Calculator

Tips: Enter the Truncated Cuboctahedron Edge length in meters. The value must be positive.

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. It has 48 faces, 72 edges, and 26 vertices.

Q2: How is the Truncated Cuboctahedron Edge defined?
A: It is the length of the edges of a Hexakis Octahedron created by truncating the vertices of a Cuboctahedron.

Q3: What units should be used for input?
A: The input should be in meters (m), and the result will be in square meters (m²).

Q4: Are there limitations to this formula?
A: The formula is specific to the Hexakis Octahedron and assumes ideal geometric conditions.

Q5: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for the Hexakis Octahedron given the Truncated Cuboctahedron Edge.