Edge Length of Snub Cube given Midsphere Radius Calculator

Formula Used:

\[ Edge Length of Snub Cube = \frac{Midsphere Radius of Snub Cube}{\sqrt{\frac{1}{4 \times (2 - [Tribonacci_C])}}} \]

Edge Length of Snub Cube:

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1. What is the Edge Length of Snub Cube given Midsphere Radius Calculation?

The Edge Length of Snub Cube given Midsphere Radius calculation determines the length of any edge of a Snub Cube based on its midsphere radius. This geometric relationship is derived from the unique properties of the Snub Cube, an Archimedean solid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Edge Length = \frac{Midsphere Radius}{\sqrt{\frac{1}{4 \times (2 - [Tribonacci_C])}}} \]

Where:

\( [Tribonacci_C] \) — Tribonacci constant (≈1.839286755214161)
Midsphere Radius — Radius of the sphere tangent to all edges of the Snub Cube

Explanation: This formula establishes the mathematical relationship between the midsphere radius and the edge length of a Snub Cube, utilizing the Tribonacci constant which appears in various geometric properties of this solid.

3. Importance of Edge Length Calculation

Details: Calculating the edge length from the midsphere radius is essential for geometric analysis, 3D modeling, and understanding the spatial properties of Snub Cubes in mathematical and architectural applications.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and non-zero. The calculator will compute the corresponding edge length of the Snub Cube.

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, known for its chiral properties.

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 accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the Snub Cube, with precision limited only by floating-point arithmetic.

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 involving the Tribonacci constant.

Q5: What are practical applications of this calculation?
A: Applications include computational geometry, 3D modeling, architectural design, and mathematical research involving polyhedral structures.