1. What is the Volume of Tetrakis Hexahedron?

The Volume of Tetrakis Hexahedron is the quantity of three-dimensional space enclosed by the entire surface of the Tetrakis Hexahedron. It is a Catalan solid that can be derived from a cube by adding square pyramids on each face.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of Tetrakis Hexahedron (m³)
• \( r_m \) — Midsphere Radius (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: The formula calculates the volume based on the midsphere radius, which is the radius of the sphere tangent to all edges of the polyhedron.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in various fields including architecture, engineering, material science, and 3D modeling. Accurate volume calculations help in determining capacity, material requirements, and structural properties.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and greater than zero. The calculator will compute the volume using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid with 24 faces, 36 edges, and 14 vertices. It can be constructed by adding square pyramids to each face of a cube.

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula is only applicable to the Tetrakis Hexahedron. Different polyhedra have different volume formulas.

Q4: What are the units of measurement?
A: The calculator uses meters for input (midsphere radius) and cubic meters for output (volume). Ensure consistent units for accurate results.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise based on the input values. The result is rounded to 6 decimal places for practical use.