1. What is the Height of Tetrakis Hexahedron?

The height of a Tetrakis Hexahedron is the vertical distance from any vertex to the face directly opposite to that vertex. It's an important geometric measurement for this Catalan solid.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of Tetrakis Hexahedron (m)
• \( TSA \) — Total Surface Area (m²)

Explanation: This formula calculates the height based on the total surface area of the Tetrakis Hexahedron, using the mathematical relationship between these geometric properties.

3. Importance of Height Calculation

Details: Calculating the height of a Tetrakis Hexahedron is essential for understanding its three-dimensional properties, volume calculations, and various applications in geometry and engineering.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and valid 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 seen as a cube with square pyramids on each face. It has 24 faces, 36 edges, and 14 vertices.

Q2: What units should I use for the calculation?
A: The calculator uses meters for length and square meters for area. Make sure to use consistent units throughout your calculation.

Q3: Can this formula be used for any Tetrakis Hexahedron?
A: Yes, this formula applies to all regular Tetrakis Hexahedrons where all pyramids added to the cube faces are identical.

Q4: What if I have the edge length instead of surface area?
A: You would need to calculate the surface area first using the appropriate formula for a Tetrakis Hexahedron before using this calculator.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values. The accuracy depends on the precision of your surface area measurement.