Volume of Snub Cube given Midsphere Radius Calculator

Formula Used:

\[ V = \frac{(3\sqrt{[Tribonacci_C]-1}) + (4\sqrt{[Tribonacci_C]+1})}{3\sqrt{2-[Tribonacci_C]}} \times \left( \frac{r_m}{\sqrt{\frac{1}{4(2-[Tribonacci_C])}}} \right)^3 \]

Volume of Snub Cube:

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1. What is the Volume of Snub Cube?

The Volume of Snub Cube is the total quantity of three dimensional space enclosed by the surface of the Snub Cube. It is an important geometric measurement in solid geometry and architectural design.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ V = \frac{(3\sqrt{[Tribonacci_C]-1}) + (4\sqrt{[Tribonacci_C]+1})}{3\sqrt{2-[Tribonacci_C]}} \times \left( \frac{r_m}{\sqrt{\frac{1}{4(2-[Tribonacci_C])}}} \right)^3 \]

Where:

\( V \) — Volume of Snub Cube (m³)
\( r_m \) — Midsphere Radius of Snub Cube (m)
\( [Tribonacci_C] \) — Tribonacci constant (1.839286755214161)

Explanation: The formula calculates the volume of a snub cube based on its midsphere radius, using the mathematical constant known as the Tribonacci constant.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is crucial in various fields including architecture, engineering, manufacturing, and mathematical research. The snub cube is an Archimedean solid with interesting geometric properties.

4. Using the Calculator

Tips: Enter the midsphere radius of the snub cube in meters. The value must be positive and valid. The calculator will compute the volume using the mathematical formula.

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. It is a semi-regular convex polyhedron.

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 is Midsphere Radius?
A: Midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q4: What are the applications of Snub Cube?
A: Snub cubes have applications in crystallography, architecture, and as mathematical models in various scientific fields.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the given formula and the Tribonacci constant value.