Edge Length of Snub Cube given Volume Calculator

Formula Used:

\[ l_e = \left( \frac{3 \cdot \sqrt{2 - C_{Tribonacci}} \cdot V}{3 \cdot \sqrt{C_{Tribonacci} - 1} + 4 \cdot \sqrt{C_{Tribonacci} + 1}} \right)^{\frac{1}{3}} \]

Edge Length of Snub Cube:

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1. What is the Edge Length of Snub Cube Formula?

The formula calculates the edge length of a snub cube given its volume, using the Tribonacci constant. The snub cube is an Archimedean solid with 38 faces (6 squares and 32 equilateral triangles).

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_e = \left( \frac{3 \cdot \sqrt{2 - C_{Tribonacci}} \cdot V}{3 \cdot \sqrt{C_{Tribonacci} - 1} + 4 \cdot \sqrt{C_{Tribonacci} + 1}} \right)^{\frac{1}{3}} \]

Where:

\( l_e \) — Edge length of the snub cube
\( V \) — Volume of the snub cube
\( C_{Tribonacci} \) — Tribonacci constant (≈1.839286755214161)

Explanation: The formula relates the volume of a snub cube to its edge length through the mathematical constant known as the Tribonacci constant.

3. Importance of Edge Length Calculation

Details: Calculating the edge length from volume is essential for geometric modeling, architectural design, and understanding the properties of this particular Archimedean solid.

4. Using the Calculator

Tips: Enter the volume of the snub cube in cubic meters. The volume must be a positive value greater than zero.

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 equilateral triangles - and 60 edges.

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: What are typical volume values for snub cubes?
A: Volume depends on the edge length. For an edge length of 1 unit, the volume is approximately 7.88948 cubic units.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the snub cube due to its unique geometric properties.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, though computational precision may introduce minor rounding errors.