Width of Elongated Dodecahedron Given Surface to Volume Ratio Calculator

Formula:

\[ w = \frac{\sqrt{3} \times (3 + \sqrt{5})}{RA/V} \]

Width of Elongated Dodecahedron:

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1. What is the Width of Elongated Dodecahedron?

The width of an elongated dodecahedron is the horizontal distance from the left most edge to the right most edge of this polyhedron. It's an important geometric measurement for understanding the spatial dimensions of this shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ w = \frac{\sqrt{3} \times (3 + \sqrt{5})}{RA/V} \]

Where:

\( w \) — Width of elongated dodecahedron (m)
\( RA/V \) — Surface to volume ratio (1/m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)
\( \sqrt{5} \) — Square root of 5 (approximately 2.236)

Explanation: This formula calculates the width based on the surface to volume ratio, using mathematical constants specific to the geometry of elongated dodecahedrons.

3. Importance of Width Calculation

Details: Calculating the width of an elongated dodecahedron is important in various fields including crystallography, materials science, and 3D modeling where this specific polyhedral shape is used.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

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 elongated shape.

Q2: How is surface to volume ratio measured?
A: Surface to volume ratio is calculated by dividing the total surface area by the volume of the shape, typically expressed in 1/m units.

Q3: What are typical values for surface to volume ratio?
A: The surface to volume ratio varies depending on the size and specific dimensions of the elongated dodecahedron, but generally decreases as the size increases.

Q4: Can this formula be used for regular dodecahedrons?
A: No, this specific formula is designed for elongated dodecahedrons and would not be accurate for regular dodecahedrons.

Q5: What precision should I use for the input values?
A: For most applications, 4 decimal places of precision is sufficient, though the calculator accepts more precise inputs if needed.