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The edge length of an elongated dodecahedron is the distance between any pair of adjacent vertices of this polyhedron. It is a fundamental geometric property used in various mathematical and engineering calculations.
The calculator uses the formula:
Where:
Explanation: This formula derives from the geometric relationship between the volume and edge length of an elongated dodecahedron, where the volume is proportional to the cube of the edge length.
Details: Calculating the edge length from volume is essential for geometric modeling, structural analysis, and various engineering applications where precise dimensional relationships are required.
Tips: Enter the volume of the elongated dodecahedron in cubic meters. The value must be positive and valid.
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 regular pentagonal faces and additional rectangular faces.
Q2: Why is the volume divided by 6 in the formula?
A: The constant 6 comes from the specific geometric properties and scaling factors of the elongated dodecahedron shape.
Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to elongated dodecahedra. Other polyhedra have different volume-to-edge-length relationships.
Q4: What are typical applications of this calculation?
A: This calculation is used in crystallography, architectural design, 3D modeling, and various engineering fields where precise geometric measurements are required.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect elongated dodecahedra. The accuracy in practical applications depends on the precision of the input volume measurement.