Cubical Edge Length of Tetrakis Hexahedron Given Surface to Volume Ratio Calculator

Formula Used:

\[ l_{e(Cube)} = \frac{2 \times \sqrt{5}}{R_{A/V}} \]

Cubical Edge Length (l_e(Cube)):

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1. What is Cubical Edge Length of Tetrakis Hexahedron?

The Cubical Edge Length of Tetrakis Hexahedron is the length of the line connecting any two adjacent vertices of cube of Tetrakis Hexahedron. It's a fundamental measurement in understanding the geometry of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{e(Cube)} = \frac{2 \times \sqrt{5}}{R_{A/V}} \]

Where:

\( l_{e(Cube)} \) — Cubical Edge Length (meters)
\( R_{A/V} \) — Surface to Volume Ratio (1/meter)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the cubical edge length based on the surface to volume ratio of the Tetrakis Hexahedron, using the mathematical constant √5.

3. Importance of Cubical Edge Length Calculation

Details: Calculating the cubical edge length is essential for understanding the geometric properties of Tetrakis Hexahedron, including its volume, surface area, and other dimensional characteristics in various mathematical and engineering applications.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/meter units. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid that is the dual polyhedron of the truncated octahedron. It has 24 faces, 36 edges, and 14 vertices.

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, typically measured in 1/length units.

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 Tetrakis Hexahedron, with smaller objects generally having higher ratios.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Tetrakis Hexahedron due to its unique geometric properties.

Q5: What units should I use for the calculation?
A: Use consistent units throughout - typically meters for length and 1/meter for surface to volume ratio.