Octahedral Edge Length Of Triakis Octahedron Given Volume Calculator

Formula Used:

\[ l_{e(Octahedron)} = \left( \frac{V}{2-\sqrt{2}} \right)^{1/3} \]

Octahedral Edge Length of Triakis Octahedron:

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1. What is Octahedral Edge Length of Triakis Octahedron?

The Octahedral Edge Length of Triakis Octahedron is the length of the line connecting any two adjacent vertices of the octahedron of Triakis Octahedron. It is a fundamental geometric property that helps define the shape and dimensions of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{e(Octahedron)} = \left( \frac{V}{2-\sqrt{2}} \right)^{1/3} \]

Where:

\( l_{e(Octahedron)} \) — Octahedral Edge Length of Triakis Octahedron (m)
\( V \) — Volume of Triakis Octahedron (m³)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the octahedral edge length from the volume of the Triakis Octahedron using the mathematical relationship between volume and edge length.

3. Importance of Octahedral Edge Length Calculation

Details: Calculating the octahedral edge length is essential for understanding the geometric properties of Triakis Octahedron, including its surface area, volume relationships, and spatial dimensions in various applications.

4. Using the Calculator

Tips: Enter the volume of Triakis Octahedron in cubic meters. The value must be positive and valid. The calculator will compute the corresponding octahedral edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Octahedron?
A: A Triakis Octahedron is a Catalan solid that can be obtained by adding a triangular pyramid on each face of a regular octahedron.

Q2: What are the units for this calculation?
A: The volume should be in cubic meters (m³) and the resulting octahedral edge length will be in meters (m).

Q3: Why is the square root of 2 used in the formula?
A: The square root of 2 appears in the formula due to the geometric relationships inherent in the octahedral structure and its volume-edge length relationship.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Triakis Octahedron and its octahedral edge length calculation.

Q5: What if I get an error in calculation?
A: Ensure that the input volume is a positive number. The calculator requires valid numerical input to perform the calculation correctly.