Total Surface Area of Tetrakis Hexahedron given Insphere Radius Calculator

Formula Used:

\[ TSA = \frac{100 \times r_i^2}{3 \times \sqrt{5}} \]

Total Surface Area of Tetrakis Hexahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Total Surface Area of Tetrakis Hexahedron?

The Total Surface Area of a Tetrakis Hexahedron is the total quantity of plane enclosed on the entire surface of this polyhedron. It's an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{100 \times r_i^2}{3 \times \sqrt{5}} \]

Where:

\( TSA \) — Total Surface Area of Tetrakis Hexahedron (m²)
\( r_i \) — Insphere Radius of Tetrakis Hexahedron (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the total surface area based on the insphere radius of the Tetrakis Hexahedron, using the mathematical constant √5 in the denominator.

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. It helps in determining material requirements, heat transfer calculations, and structural analysis.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and greater than zero. The calculator will compute the total surface area using the mathematical formula.

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 insphere radius?
A: The insphere radius is the radius of the largest sphere that can be contained within the Tetrakis Hexahedron, touching all its faces.

Q3: What units should I use for the input?
A: The calculator uses meters for the insphere radius input and returns square meters for the surface area output.

Q4: Can this formula be used for any Tetrakis Hexahedron?
A: Yes, this formula applies to all regular Tetrakis Hexahedrons where the insphere radius is known.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact based on the input value, with results rounded to 6 decimal places for precision.