1. What Is The Tetrakis Hexahedron?

The Tetrakis Hexahedron is a Catalan solid that can be derived from a cube by adding a square pyramid on each face. It has 24 isosceles triangular faces, 36 edges, and 14 vertices.

2. How Does The Calculator Work?

The calculator uses the formula:

Where:

• \( TSA \) — Total Surface Area of Tetrakis Hexahedron (m²)
• \( r_m \) — Midsphere Radius of Tetrakis Hexahedron (m)
• \( \sqrt{5} \) — Mathematical constant (approximately 2.23607)

Explanation: This formula calculates the total surface area of a Tetrakis Hexahedron based on its midsphere radius, which is the radius of the sphere tangent to all edges of the polyhedron.

3. Importance Of Total Surface Area Calculation

Details: Calculating the total surface area is important in various applications including material science, architecture, and 3D modeling where the Tetrakis Hexahedron shape is used.

4. Using The Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q2: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Tetrakis Hexahedron. Other polyhedra have different surface area formulas.

Q3: What are the units of measurement?
A: The calculator uses meters for input and square meters for output, but the formula works with any consistent unit system.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact when using the precise midsphere radius measurement.

Q5: What if I have the edge length instead of midsphere radius?
A: You would need to use a different formula that calculates surface area directly from edge length, or first convert edge length to midsphere radius.