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The short edge of a pentagonal trapezohedron is the length of any of the shorter edges of this geometric solid. It is related to the long edge through a mathematical formula based on the golden ratio.
The calculator uses the formula:
Where:
Explanation: This formula utilizes the mathematical relationship between the short and long edges of a pentagonal trapezohedron, which is derived from the golden ratio properties.
Details: Calculating the short edge is essential for geometric modeling, architectural design, and understanding the properties of pentagonal trapezohedrons in various applications.
Tips: Enter the long edge measurement in meters. The value must be positive and valid. The calculator will compute the corresponding short edge length.
Q1: What is a pentagonal trapezohedron?
A: A pentagonal trapezohedron is a polyhedron with ten faces, each of which is a kite shape, arranged in two sets of five around the polar axis.
Q2: Why does this formula involve the square root of 5?
A: The formula involves \(\sqrt{5}\) because it relates to the golden ratio (\(\phi = \frac{1+\sqrt{5}}{2}\)), which appears naturally in pentagonal symmetry.
Q3: What are typical applications of this calculation?
A: This calculation is used in geometry, crystallography, and the design of objects with pentagonal symmetry such as certain types of dice and architectural elements.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to pentagonal trapezohedrons due to their unique geometric properties.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact, though the result may be rounded for practical applications depending on the required precision.