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The edge length of an elongated dodecahedron is the distance between any pair of adjacent peak vertices of the polyhedron. It is a fundamental geometric property used in various mathematical and engineering applications.
The calculator uses the formula:
Where:
Explanation: The edge length is exactly one-third of the total width of the elongated dodecahedron, providing a simple linear relationship between these two geometric properties.
Details: Calculating the edge length is essential for understanding the geometric properties of elongated dodecahedrons, including surface area, volume calculations, and structural analysis in various applications.
Tips: Enter the width of the elongated dodecahedron in meters. The value must be positive and valid for accurate calculation.
Q1: What is an elongated dodecahedron?
A: An elongated dodecahedron is a polyhedron formed by elongating a regular dodecahedron along one of its axes, creating a prism-like structure with dodecahedral bases.
Q2: Why is the edge length exactly one-third of the width?
A: This relationship is derived from the geometric symmetry and proportional relationships inherent in the elongated dodecahedron's structure.
Q3: Can this formula be used for all elongated dodecahedrons?
A: Yes, this formula applies to all regular elongated dodecahedrons where the elongation follows the standard geometric proportions.
Q4: What are practical applications of this calculation?
A: This calculation is used in crystallography, architectural design, 3D modeling, and mathematical research involving polyhedral structures.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for ideal geometric shapes, though real-world measurements may introduce minor variations.