Tetrahedral Edge Length of Triakis Tetrahedron Given Volume Calculator

Formula Used:

\[ le(Tetrahedron) = \left(\frac{20 \times V}{3 \times \sqrt{2}}\right)^{\frac{1}{3}} \]

Tetrahedral Edge Length of Triakis Tetrahedron:

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1. What is Tetrahedral Edge Length of Triakis Tetrahedron?

The Tetrahedral Edge Length of Triakis Tetrahedron is the length of the line connecting any two adjacent vertices of tetrahedron of Triakis Tetrahedron. It is a fundamental geometric measurement in polyhedral studies.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ le(Tetrahedron) = \left(\frac{20 \times V}{3 \times \sqrt{2}}\right)^{\frac{1}{3}} \]

Where:

\( le(Tetrahedron) \) — Tetrahedral Edge Length of Triakis Tetrahedron (m)
\( V \) — Volume of Triakis Tetrahedron (m³)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the tetrahedral edge length based on the volume of the Triakis Tetrahedron, using the mathematical relationship between volume and edge length in this specific polyhedral structure.

3. Importance of Tetrahedral Edge Length Calculation

Details: Calculating the tetrahedral edge length is essential for geometric analysis, structural design, and understanding the spatial properties of Triakis Tetrahedron in various mathematical and engineering applications.

4. Using the Calculator

Tips: Enter the volume of Triakis Tetrahedron in cubic meters. The value must be positive and valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Tetrahedron?
A: A Triakis Tetrahedron is a Catalan solid that can be seen as a tetrahedron with triangular pyramids added to each face.

Q2: What are the units for this calculation?
A: The input volume should be in cubic meters (m³), and the result will be in meters (m).

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Triakis Tetrahedron due to its unique geometric properties.

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

Q5: Are there any limitations to this calculation?
A: The formula assumes a perfect geometric Triakis Tetrahedron and may not account for manufacturing tolerances or material properties in practical applications.