Formula Used:
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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.
The calculator uses the mathematical formula:
Where:
Explanation: This formula calculates the height based on the known length of the long edge, using geometric relationships and square root functions.
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.
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.
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.