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 formula:

Where:

• \( TSA \) — Total Surface Area of Tetrakis Hexahedron (m²)
• \( RA/V \) — Surface to Volume Ratio of Tetrakis Hexahedron (1/m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the total surface area based on the surface to volume ratio of the Tetrakis Hexahedron.

3. Importance of Surface Area Calculation

Details: Calculating the total surface area of geometric solids is crucial in various fields including architecture, materials science, and engineering for determining material requirements, heat transfer properties, and structural integrity.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid with 24 triangular faces, formed by attaching square pyramids to each face of a cube.

Q2: How is surface to volume ratio defined?
A: Surface to volume ratio is the ratio of the total surface area to the volume of a three-dimensional object, measured in 1/m.

Q3: What are typical applications of this calculation?
A: This calculation is used in crystallography, nanotechnology, and materials engineering where surface properties relative to volume are important.

Q4: Are there limitations to this formula?
A: This formula is specific to the Tetrakis Hexahedron shape and assumes perfect geometric proportions.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the base unit. For other units, appropriate conversion factors must be applied to the input values.