1. What is the Tetrakis Hexahedron?

The Tetrakis Hexahedron is a Catalan solid that can be seen as a cube with square pyramids attached to each face. It has 24 faces, 36 edges, and 14 vertices.

2. How Does the Calculator Work?

The calculator uses the Tetrakis Hexahedron formula:

Where:

• \( TSA \) — Total Surface Area
• \( l_{cube} \) — Cubical edge length
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: The formula calculates the total surface area by multiplying the square of the cubical edge length by 3 and the square root of 5.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of geometric solids is crucial in various fields including architecture, engineering, material science, and 3D modeling for determining material requirements, heat transfer properties, and structural analysis.

4. Using the Calculator

Tips: Enter the cubical edge length in meters. The value must be positive and greater than zero. The calculator will compute the total surface area in square meters.

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid that consists of 24 isosceles triangular faces and can be derived from a cube by adding square pyramids to each face.

Q2: How many faces does a Tetrakis Hexahedron have?
A: A Tetrakis Hexahedron has 24 triangular faces.

Q3: What are the applications of Tetrakis Hexahedron?
A: This shape is used in architecture, crystallography, and as dice in some board games due to its symmetrical properties.

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: Is the Tetrakis Hexahedron a regular polyhedron?
A: No, it's a Catalan solid, which means it's the dual of an Archimedean solid (in this case, the truncated octahedron).