Edge Length of Snub Cube given Surface to Volume Ratio Calculator

Formula Used:

\[ l_e = \frac{2 \times (3 + 4 \times \sqrt{3})}{\frac{R_A}{V} \times \frac{(3 \times \sqrt{[Tribonacci_C] - 1}) + (4 \times \sqrt{[Tribonacci_C] + 1})}{3 \times \sqrt{2 - [Tribonacci_C]}}} \]

Edge Length of Snub Cube:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Edge Length of Snub Cube?

The edge length of a snub cube is the measurement of any edge of this Archimedean solid. A snub cube is a polyhedron with 38 faces: 6 squares and 32 equilateral triangles. It has 60 edges and 24 vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_e = \frac{2 \times (3 + 4 \times \sqrt{3})}{\frac{R_A}{V} \times \frac{(3 \times \sqrt{[Tribonacci_C] - 1}) + (4 \times \sqrt{[Tribonacci_C] + 1})}{3 \times \sqrt{2 - [Tribonacci_C]}}} \]

Where:

\( l_e \) — Edge length of snub cube
\( \frac{R_A}{V} \) — Surface to volume ratio of snub cube
\( [Tribonacci_C] \) — Tribonacci constant (≈1.839286755214161)
\( \sqrt{} \) — Square root function

Explanation: This formula relates the edge length of a snub cube to its surface-to-volume ratio using the mathematical constant Tribonacci_C.

3. Importance of Edge Length Calculation

Details: Calculating the edge length of a snub cube is important in geometry, crystallography, and materials science for understanding the spatial properties and packing efficiency of this particular polyhedral structure.

4. Using the Calculator

Tips: Enter the surface-to-volume ratio of the snub cube in 1/m. The value must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a snub cube?
A: A snub cube is an Archimedean solid with 38 faces (6 squares and 32 triangles), 60 edges, and 24 vertices.

Q2: What is the Tribonacci constant?
A: The Tribonacci constant is the real root of the equation x³ - x² - x - 1 = 0, approximately equal to 1.839286755214161.

Q3: How is surface-to-volume ratio defined for a snub cube?
A: Surface-to-volume ratio is the total surface area of the snub cube divided by its volume.

Q4: What are typical applications of snub cube geometry?
A: Snub cube geometry finds applications in crystallography, molecular modeling, and architectural design.

Q5: Are there any limitations to this calculation?
A: This calculation assumes a perfect snub cube geometry and may not account for manufacturing tolerances or material properties in physical implementations.