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The width of an elongated dodecahedron is the horizontal distance from the leftmost edge to the rightmost edge of this polyhedron. It is an important geometric measurement that helps in understanding the spatial dimensions and proportions of this three-dimensional shape.
The calculator uses the formula:
Where:
Explanation: This formula establishes a direct proportional relationship between the width and height of an elongated dodecahedron, where the width is exactly √3 times the height.
Details: Calculating the width of an elongated dodecahedron is essential for various applications in geometry, architecture, engineering, and 3D modeling. It helps in determining the complete dimensional profile of the shape and ensures proper scaling in design applications.
Tips: Enter the height of the elongated dodecahedron in meters. The value must be positive and greater than zero. The calculator will automatically compute the corresponding width using the established mathematical relationship.
Q1: Why is the width exactly √3 times the height?
A: This relationship comes from the geometric properties and symmetry of the elongated dodecahedron shape, where the width-to-height ratio is constant at √3.
Q2: Can this formula be used for all elongated dodecahedrons?
A: Yes, this formula applies to all regular elongated dodecahedrons as it's derived from their fundamental geometric properties.
Q3: What units should I use for the measurements?
A: The calculator uses meters, but the formula works with any consistent unit system (cm, mm, inches, etc.) as long as both width and height use the same units.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect elongated dodecahedrons. The accuracy depends on the precision of the input height measurement.
Q5: Can I calculate height from width using this formula?
A: Yes, you can rearrange the formula to calculate height from width: \( h = \frac{w}{\sqrt{3}} \).