Pyramidal Edge Length of Tetrakis Hexahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ l_{pyramid} = \frac{3 \times \sqrt{5}}{2 \times \frac{A}{V}} \]

Pyramidal Edge Length:

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1. What is Pyramidal Edge Length of Tetrakis Hexahedron?

The Pyramidal Edge Length of Tetrakis Hexahedron refers to the length of the edges that form the pyramidal components of this polyhedron. The Tetrakis Hexahedron is a Catalan solid derived from the cube by adding a square pyramid on each face.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{pyramid} = \frac{3 \times \sqrt{5}}{2 \times \frac{A}{V}} \]

Where:

\( l_{pyramid} \) — Pyramidal Edge Length (m)
\( \frac{A}{V} \) — Surface to Volume Ratio (m⁻¹)
\( \sqrt{5} \) — Mathematical constant (approximately 2.23607)

Explanation: This formula calculates the pyramidal edge length based on the surface to volume ratio of the Tetrakis Hexahedron, utilizing the mathematical relationship between these geometric properties.

3. Importance of Pyramidal Edge Length Calculation

Details: Calculating the pyramidal edge length is essential for understanding the geometric properties of the Tetrakis Hexahedron, including its surface area, volume, and overall structural characteristics. This calculation is particularly important in crystallography, materials science, and architectural design where precise geometric measurements are required.

4. Using the Calculator

Tips: Enter the surface to volume ratio in m⁻¹. The value must be positive and greater than zero. The calculator will compute the corresponding pyramidal edge length in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid that can be formed by adding a square pyramid to each face of a cube. It has 24 faces, 36 edges, and 14 vertices.

Q2: How is the surface to volume ratio defined?
A: The surface to volume ratio (A/V) is the total surface area of the polyhedron divided by its volume, measured in m⁻¹.

Q3: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the size and proportions of the Tetrakis Hexahedron. Smaller polyhedra generally have higher surface to volume ratios.

Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula applies only to the Tetrakis Hexahedron. Other polyhedra have different geometric relationships.

Q5: What units should I use for input and output?
A: Input should be in m⁻¹ (surface to volume ratio) and output will be in meters (pyramidal edge length). Ensure consistent units throughout your calculations.