Total Surface Area of Tetrakis Hexahedron given Height Calculator

Tetrakis Hexahedron Surface Area Formula:

\[ TSA = \frac{4 \times \sqrt{5}}{3} \times h^2 \]

Total Surface Area (TSA):

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1. What is the Tetrakis Hexahedron?

The Tetrakis Hexahedron is a Catalan solid that is the dual of the truncated octahedron. It has 24 faces, 36 edges, and 14 vertices. Each face is an isosceles triangle.

2. How Does the Calculator Work?

The calculator uses the surface area formula:

\[ TSA = \frac{4 \times \sqrt{5}}{3} \times h^2 \]

Where:

\( TSA \) — Total Surface Area (m²)
\( h \) — Height of Tetrakis Hexahedron (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: The formula calculates the total surface area based on the height measurement of the Tetrakis Hexahedron.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of geometric solids is essential in various fields including architecture, engineering, material science, and 3D modeling for determining material requirements, heat transfer calculations, and structural analysis.

4. Using the Calculator

Tips: Enter the height of the Tetrakis Hexahedron in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between height and edge length?
A: The height of a Tetrakis Hexahedron is related to its edge length through specific geometric proportions that maintain the solid's symmetry.

Q2: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Tetrakis Hexahedron. Other polyhedra have different surface area formulas based on their unique geometry.

Q3: How accurate is this calculation?
A: The calculation is mathematically exact when using the precise formula, though practical measurements may introduce some error.

Q4: What are practical applications of this calculation?
A: This calculation is useful in crystallography, architectural design, 3D printing, and any application involving the construction or analysis of this specific geometric shape.

Q5: How does the surface area relate to volume?
A: While surface area and volume are related through the geometry of the solid, they represent different properties and have separate calculation formulas.