Total Surface Area Of Triakis Tetrahedron Given Midsphere Radius Calculator

Formula Used:

\[ TSA = \frac{3}{5} \times \sqrt{11} \times \left( \frac{4 \times r_m}{\sqrt{2}} \right)^2 \]

Total Surface Area of Triakis Tetrahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Total Surface Area of Triakis Tetrahedron?

The Total Surface Area of a Triakis Tetrahedron is the total area of all the faces of the polyhedron. A Triakis Tetrahedron is a Catalan solid that can be constructed by attaching a triangular pyramid to each face of a regular tetrahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{3}{5} \times \sqrt{11} \times \left( \frac{4 \times r_m}{\sqrt{2}} \right)^2 \]

Where:

\( TSA \) — Total Surface Area of Triakis Tetrahedron (m²)
\( r_m \) — Midsphere Radius of Triakis Tetrahedron (m)
\( \sqrt{11} \) — Square root of 11 (approximately 3.3166)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the total surface area based on the midsphere radius of the Triakis Tetrahedron, using geometric relationships specific to this polyhedron.

3. Importance of Surface Area Calculation

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

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Tetrahedron?
A: A Triakis Tetrahedron is a Catalan solid that results from attaching a triangular pyramid to each face of a regular tetrahedron. It has 12 faces, 18 edges, and 8 vertices.

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of a sphere that is tangent to all the edges of the polyhedron.

Q3: Can this calculator handle different units?
A: The calculator assumes input in meters and outputs in square meters. For other units, convert your measurements to meters first.

Q4: What is the precision of the calculation?
A: The calculator provides results with 6 decimal places precision for accurate measurements.

Q5: Are there other ways to calculate surface area?
A: Yes, surface area can also be calculated using edge length or other geometric properties, but this calculator specifically uses the midsphere radius.