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The edge length of an elongated dodecahedron is the distance between any pair of adjacent peak vertices of this polyhedron. It's a fundamental geometric measurement used in various mathematical and engineering applications.
The calculator uses the formula:
Where:
Explanation: This formula calculates the edge length based on the total surface area of the elongated dodecahedron, using mathematical constants and geometric relationships.
Details: Calculating the edge length is crucial for understanding the geometric properties of elongated dodecahedrons, including volume calculations, structural analysis, and various applications in architecture and engineering design.
Tips: Enter the total surface area in square meters. The value must be positive and greater than zero 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 shape with 12 pentagonal faces and additional rectangular faces.
Q2: Why is this specific formula used?
A: This formula derives from the geometric relationships between the edge length and total surface area of an elongated dodecahedron, incorporating mathematical constants that represent the shape's properties.
Q3: What units should be used for input?
A: The calculator uses square meters for surface area input and returns meters for edge length output. Consistent units must be maintained throughout the calculation.
Q4: Are there limitations to this calculation?
A: This calculation assumes a perfect geometric elongated dodecahedron. Real-world applications may require adjustments for material properties, manufacturing tolerances, or other practical considerations.
Q5: Can this calculator handle very large or very small values?
A: The calculator can handle a wide range of values, but extremely large or small numbers may be limited by PHP's floating-point precision capabilities.