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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 is a fundamental geometric property used in various mathematical and engineering applications.
The calculator uses the mathematical formula:
Where:
Explanation: This formula establishes the precise mathematical relationship between the height and edge length of an elongated dodecahedron based on its geometric properties.
Details: Calculating the edge length is essential for understanding the geometric properties of elongated dodecahedrons, which have applications in crystallography, architecture, and mathematical modeling of three-dimensional structures.
Tips: Enter the height of the elongated dodecahedron in meters. The value must be positive and valid. The calculator will compute the corresponding edge length using the mathematical relationship.
Q1: What is an elongated dodecahedron?
A: An elongated dodecahedron is a polyhedron with 12 faces that has been stretched along one axis, creating a distinctive geometric shape with specific mathematical properties.
Q2: Why is the square root of 3 used in this formula?
A: The square root of 3 appears due to the geometric relationships and trigonometric properties inherent in the structure of the elongated dodecahedron.
Q3: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to elongated dodecahedrons. Other polyhedrons have different mathematical relationships between their dimensions.
Q4: What are typical applications of elongated dodecahedrons?
A: They are used in crystallography to describe certain crystal structures, in architectural design for creating unique spatial forms, and in mathematical research on polyhedral geometry.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of elongated dodecahedrons, assuming precise input values.