1. What is the Tetrakis Hexahedron Volume Formula?

The Tetrakis Hexahedron volume formula calculates the volume of a Tetrakis Hexahedron given its insphere radius. A Tetrakis Hexahedron is a Catalan solid that can be seen as a cube with square pyramids on each face.

2. How Does the Calculator Work?

The calculator uses the Tetrakis Hexahedron volume formula:

Where:

• \( V \) — Volume of Tetrakis Hexahedron (m³)
• \( r_i \) — Insphere radius (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: The formula calculates the volume based on the relationship between the insphere radius and the geometric properties of the Tetrakis Hexahedron.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for understanding the spatial properties of the Tetrakis Hexahedron, material requirements, and various engineering applications involving this specific geometric shape.

4. Using the Calculator

Tips: Enter the insphere radius in meters. 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 that can be constructed by adding square pyramids to each face of a cube. It has 24 faces, 36 edges, and 14 vertices.

Q2: What is the insphere radius?
A: The insphere radius is the radius of the largest sphere that can fit inside the Tetrakis Hexahedron, touching all its faces.

Q3: How accurate is this formula?
A: The formula provides an exact mathematical relationship between the insphere radius and volume of a perfect Tetrakis Hexahedron.

Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters first or adjust the result accordingly.

Q5: What are practical applications of this calculation?
A: This calculation is useful in crystallography, architecture, 3D modeling, and any field dealing with complex polyhedral structures.