1. What is Insphere Radius of Tetrakis Hexahedron?

The Insphere Radius of a Tetrakis Hexahedron is the radius of the largest sphere that can be contained within the polyhedron such that it touches all the faces of the Tetrakis Hexahedron tangentially.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere Radius (m)
• \( TSA \) — Total Surface Area of Tetrakis Hexahedron (m²)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the radius of the inscribed sphere based on the total surface area of the Tetrakis Hexahedron.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and material science for understanding the spatial properties and packing efficiency of the Tetrakis Hexahedron shape.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid that is the dual of the truncated octahedron, with 24 isosceles triangular faces.

Q2: What units should I use for the input?
A: The calculator expects the total surface area in square meters (m²), and returns the insphere radius in meters (m).

Q3: Can this calculator handle very large or very small values?
A: Yes, as long as the input is a positive number, the calculator can process it, though extremely large values may require scientific notation.

Q4: What if I get an error or unexpected result?
A: Ensure that the input value is a positive number. Negative values or zero are not valid for surface area.

Q5: Is this formula applicable to all polyhedrons?
A: No, this specific formula is derived for the Tetrakis Hexahedron and may not apply to other polyhedral shapes.