1. What is the Volume of 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. The volume calculation is essential in geometry and 3D modeling.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of Tetrakis Hexahedron (m³)
• \( RA/V \) — Surface to Volume Ratio (1/m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

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

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for material estimation, structural analysis, and understanding the geometric properties of the Tetrakis Hexahedron in various applications.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. The value must be greater than 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid with 24 congruent isosceles triangular faces, 36 edges, and 14 vertices.

Q2: What is the significance of surface to volume ratio?
A: The surface to volume ratio is important in determining how the shape interacts with its environment, particularly in heat transfer and chemical reactions.

Q3: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for the Tetrakis Hexahedron. Other polyhedra have different volume formulas.

Q4: What are the units for volume?
A: The volume is calculated in cubic meters (m³). Make sure your input units are consistent.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the provided formula. The accuracy depends on the precision of the input value.