Total Surface Area of Tetrakis Hexahedron given Volume Calculator

Formula Used:

\[ TSA = 3 \times \sqrt{5} \times \left( \frac{2 \times V}{3} \right)^{2/3} \]

Total Surface Area of Tetrakis Hexahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Tetrakis Hexahedron?

The Tetrakis Hexahedron is a Catalan solid that is the dual of the truncated octahedron. It has 24 isosceles triangular faces, 36 edges, and 14 vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 3 \times \sqrt{5} \times \left( \frac{2 \times V}{3} \right)^{2/3} \]

Where:

\( TSA \) — Total Surface Area of Tetrakis Hexahedron (m²)
\( V \) — Volume of Tetrakis Hexahedron (m³)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the total surface area of a Tetrakis Hexahedron based on its volume, using the mathematical relationship between these two properties.

3. Importance of Surface Area Calculation

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

4. Using the Calculator

Tips: Enter the volume of the Tetrakis Hexahedron in cubic meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for volume input?
A: The calculator expects volume input in cubic meters (m³). If you have measurements in other units, convert them to cubic meters first.

Q2: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the Tetrakis Hexahedron. The result is rounded to 6 decimal places for practical use.

Q3: Can this formula be used for any Tetrakis Hexahedron?
A: Yes, this formula applies to all regular Tetrakis Hexahedrons regardless of size, as long as the shape maintains its perfect geometric properties.

Q4: What are some real-world applications of Tetrakis Hexahedrons?
A: Tetrakis Hexahedrons are used in crystallography, architectural design, and as dice in some tabletop games due to their interesting geometric properties.

Q5: How is this different from a regular hexahedron (cube)?
A: While both are polyhedrons, the Tetrakis Hexahedron has 24 triangular faces compared to the cube's 6 square faces, and different symmetry properties.