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Height of Tetragonal Trapezohedron given Long Edge Calculator

Formula Used:

\[ h = \sqrt{\frac{1}{2} \times (4 + 3 \times \sqrt{2})} \times \frac{2 \times l_{long}}{\sqrt{2 \times (1 + \sqrt{2})}} \]

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1. What is the Height of Tetragonal Trapezohedron?

The height of a Tetragonal Trapezohedron is the vertical distance between the two peak vertices where the long edges join. It is an important geometric measurement that helps define the three-dimensional structure of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ h = \sqrt{\frac{1}{2} \times (4 + 3 \times \sqrt{2})} \times \frac{2 \times l_{long}}{\sqrt{2 \times (1 + \sqrt{2})}} \]

Where:

Explanation: This formula calculates the height based on the known length of the long edge, using geometric relationships and square root functions.

3. Importance of Height Calculation

Details: Calculating the height is essential for understanding the complete geometry of the Tetragonal Trapezohedron, which is important in crystallography, material science, and geometric modeling applications.

4. Using the Calculator

Tips: Enter the length of the long edge in meters. The value must be positive and greater than zero. The calculator will compute the corresponding height of the Tetragonal Trapezohedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetragonal Trapezohedron?
A: A Tetragonal Trapezohedron is a polyhedron with trapezoidal faces that is part of the trapezohedron family, characterized by its specific symmetry and geometric properties.

Q2: Why is the formula so complex?
A: The formula involves square roots and constants derived from the geometric relationships between the edges and height in this specific polyhedral structure.

Q3: What are typical values for the long edge?
A: The long edge length can vary depending on the specific Tetragonal Trapezohedron, but it must always be a positive value greater than zero.

Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for calculating the height of a Tetragonal Trapezohedron given its long edge length.

Q5: How accurate are the results?
A: The results are mathematically precise based on the input value, with calculations performed to 10 decimal places for accuracy.

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