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The width of an elongated dodecahedron is the horizontal distance from the leftmost edge to the rightmost edge of this three-dimensional geometric shape. It represents one of the key dimensional measurements of this polyhedron.
The calculator uses the mathematical formula:
Where:
Explanation: This formula calculates the width based on the volume of the elongated dodecahedron using cube root relationship, scaled by the constant factor of 3.
Details: Calculating the width from volume is essential in geometric modeling, architectural design, and material science where precise dimensional relationships of polyhedral structures need to be determined.
Tips: Enter the volume of the elongated dodecahedron in cubic 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 with 12 faces that has been stretched along one axis, creating a longer dimension while maintaining its dodecahedral characteristics.
Q2: Why is the formula w = 3*(V/6)^(1/3) used?
A: This formula derives from the geometric properties and volume-to-dimension relationships specific to elongated dodecahedrons, where the width scales with the cube root of volume.
Q3: What units should be used for volume input?
A: The calculator expects volume in cubic meters (m³), but you can use any consistent unit system as long as the width output will be in the corresponding linear units.
Q4: Can this calculator handle very large or very small volumes?
A: Yes, the calculator can process a wide range of volume values, though extremely large or small numbers may be limited by computational precision.
Q5: Is this formula applicable to all types of dodecahedrons?
A: No, this specific formula applies only to elongated dodecahedrons. Regular dodecahedrons and other variations have different dimensional relationships.