1. What is the Midsphere Radius of Tetrakis Hexahedron?

The Midsphere Radius of Tetrakis Hexahedron is the radius of the sphere for which all the edges of the Tetrakis Hexahedron become a tangent line on that sphere. It is an important geometric property in three-dimensional space.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_m \) — Midsphere Radius of Tetrakis Hexahedron (m)
• \( TSA \) — Total Surface Area of Tetrakis Hexahedron (m²)

Explanation: This formula calculates the midsphere radius based on the total surface area of the Tetrakis Hexahedron, using mathematical constants and square root functions.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is crucial for understanding the geometric properties of the Tetrakis Hexahedron, its spatial relationships, and for applications in various fields including mathematics, engineering, and 3D modeling.

4. Using the Calculator

Tips: Enter the total surface area of the Tetrakis Hexahedron in square meters. The value must be positive and valid.

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. It has 24 faces, 36 edges, and 14 vertices.

Q2: What is the significance of the midsphere?
A: The midsphere (or intersphere) is a sphere that is tangent to all edges of a polyhedron, providing important geometric information about the shape.

Q3: How accurate is this calculation?
A: The calculation is mathematically precise based on the given formula, assuming accurate input values.

Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula applies only to the Tetrakis Hexahedron. Other polyhedra have different formulas for calculating their midsphere radii.

Q5: What are the units for the result?
A: The result is given in meters (m), which is consistent with the input unit for surface area (m²).