Edge Length of Truncated Cuboctahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ l_e = \frac{6 \times (2 + \sqrt{2} + \sqrt{3})}{R_{A/V} \times (11 + 7 \times \sqrt{2})} \]

Edge Length (l_e):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Edge Length of Truncated Cuboctahedron?

The edge length of a truncated cuboctahedron is the length of any edge of this Archimedean solid. It is a fundamental geometric property used in various mathematical and engineering calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_e = \frac{6 \times (2 + \sqrt{2} + \sqrt{3})}{R_{A/V} \times (11 + 7 \times \sqrt{2})} \]

Where:

\( l_e \) — Edge length of the truncated cuboctahedron (m)
\( R_{A/V} \) — Surface to volume ratio of the truncated cuboctahedron (m⁻¹)
\( \sqrt{2} \) — Square root of 2 (≈1.4142)
\( \sqrt{3} \) — Square root of 3 (≈1.7321)

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

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for determining various geometric properties of the truncated cuboctahedron, including surface area, volume, and other dimensional characteristics used in mathematical modeling and engineering applications.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated cuboctahedron?
A: A truncated cuboctahedron is an Archimedean solid with 26 faces: 12 squares, 8 regular hexagons, and 6 regular octagons.

Q2: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the size of the polyhedron. Smaller polyhedra typically have higher surface to volume ratios.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the truncated cuboctahedron due to its unique geometric properties.

Q4: What are the practical applications of this calculation?
A: This calculation is used in geometry, crystallography, material science, and architectural design where truncated cuboctahedron shapes are employed.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, though the precision of the result depends on the accuracy of the input value and the computational precision.