Edge Length of Snub Disphenoid given Surface to Volume Ratio Calculator

Formula Used:

\[ l_e = \frac{3\sqrt{3}}{0.85949364619130053 \times \frac{A}{V}} \]

Edge Length of Snub Disphenoid (lₑ):

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1. What is the Edge Length of Snub Disphenoid?

The Edge Length of Snub Disphenoid is the length of any edge of a Snub Disphenoid, which is a polyhedron with 12 equilateral triangle faces and 18 edges. It is an important geometric parameter in three-dimensional geometry.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_e = \frac{3\sqrt{3}}{0.85949364619130053 \times \frac{A}{V}} \]

Where:

\( l_e \) — Edge Length of Snub Disphenoid (m)
\( \frac{A}{V} \) — Surface to Volume Ratio of Snub Disphenoid (1/m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)
0.85949364619130053 — Constant specific to Snub Disphenoid geometry

Explanation: This formula relates the edge length to the surface-to-volume ratio through a specific geometric constant for Snub Disphenoids.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is crucial for understanding the geometric properties, volume, surface area, and other characteristics of Snub Disphenoids in mathematical and engineering applications.

4. Using the Calculator

Tips: Enter the surface-to-volume ratio in 1/m. The value must be greater than 0. The calculator will compute the corresponding edge length in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is a Snub Disphenoid?
A: A Snub Disphenoid is a convex polyhedron with 12 equilateral triangle faces, 18 edges, and 8 vertices. It is one of the Johnson solids.

Q2: Why is the constant 0.85949364619130053 used?
A: This constant is derived from the specific geometric properties of the Snub Disphenoid and relates its surface area to volume ratio to its edge length.

Q3: What are typical values for surface-to-volume ratio?
A: The surface-to-volume ratio depends on the size of the Snub Disphenoid. Smaller polyhedra have higher ratios, while larger ones have lower ratios.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula and constant are only applicable to Snub Disphenoids due to their unique geometric properties.

Q5: What units should I use?
A: The calculator uses meters for length and 1/m for surface-to-volume ratio. Ensure consistent units for accurate results.