Octahedral Edge Length of Triakis Octahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ l_{e(Octahedron)} = \frac{6 \times \sqrt{23 - (16 \times \sqrt{2})}}{(2 - \sqrt{2}) \times R_{A/V}} \]

Octahedral Edge Length of Triakis Octahedron:

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1. What is the 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 measurement in the study of this particular polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{e(Octahedron)} = \frac{6 \times \sqrt{23 - (16 \times \sqrt{2})}}{(2 - \sqrt{2}) \times R_{A/V}} \]

Where:

\( l_{e(Octahedron)} \) — Octahedral Edge Length of Triakis Octahedron (m)
\( R_{A/V} \) — Surface to Volume Ratio of Triakis Octahedron (1/m)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the octahedral edge length based on the surface to volume ratio of the Triakis Octahedron, incorporating geometric constants and square root operations.

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, and other dimensional characteristics in mathematical and engineering applications.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. The value must be positive and valid for accurate calculation of the octahedral edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Octahedron?
A: A Triakis Octahedron is a polyhedron created by attaching a triangular pyramid to each face of a regular octahedron, resulting in a Catalan solid with 24 isosceles triangular faces.

Q2: How is surface to volume ratio defined?
A: Surface to volume ratio is the numerical ratio of the total surface area of a solid to its volume, representing how much surface area exists per unit volume.

Q3: What are typical values for surface to volume ratio?
A: The surface to volume ratio varies depending on the size and shape of the Triakis Octahedron, with smaller objects generally having higher ratios.

Q4: Can this calculator handle different units?
A: The calculator uses meters for length units. Ensure consistent units when inputting values and interpreting results.

Q5: What are the geometric constants in the formula?
A: The constants 6, 23, 16, and 2 are derived from the geometric properties of the Triakis Octahedron and its relationship to the regular octahedron.