Edge Length of Rhombicuboctahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ l_e = \frac{3 \times (9 + \sqrt{3})}{R_{A/V} \times (6 + 5 \times \sqrt{2})} \]

Edge Length (l_e):

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1. What is the Edge Length of Rhombicuboctahedron?

The edge length of a Rhombicuboctahedron is the measurement of any edge of this Archimedean solid. It's a fundamental geometric property used in various mathematical and engineering calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_e = \frac{3 \times (9 + \sqrt{3})}{R_{A/V} \times (6 + 5 \times \sqrt{2})} \]

Where:

\( l_e \) — Edge Length of Rhombicuboctahedron (m)
\( R_{A/V} \) — Surface to Volume Ratio (1/m)
\( \sqrt{3} \) — Square root of 3 (≈1.732)
\( \sqrt{2} \) — Square root of 2 (≈1.414)

Explanation: This formula calculates the edge length based on the surface to volume ratio of the Rhombicuboctahedron, using mathematical constants and geometric relationships.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is crucial for understanding the geometric properties of Rhombicuboctahedrons, including surface area, volume, and other dimensional characteristics in mathematical modeling and architectural applications.

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 a Rhombicuboctahedron?
A: A Rhombicuboctahedron is an Archimedean solid with 8 triangular and 18 square faces, 24 identical vertices, and 48 edges.

Q2: What are typical values for surface to volume ratio?
A: The surface to volume ratio varies depending on the size of the Rhombicuboctahedron, with smaller objects having higher ratios.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the base unit. Ensure consistent units for accurate results.

Q4: What is the significance of the mathematical constants in the formula?
A: √2 and √3 are fundamental mathematical constants that arise from the geometric relationships within the Rhombicuboctahedron structure.

Q5: Are there limitations to this calculation?
A: This calculation assumes a perfect Rhombicuboctahedron shape and may not account for manufacturing tolerances or material properties in real-world applications.