Circumsphere Radius of Snub Cube Calculator

Circumsphere Radius of Snub Cube Formula:

\[ R_c = \sqrt{\frac{3 - C}{4(2 - C)}} \times l_e \]

Circumsphere Radius of Snub Cube (Rₑ):

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1. What is the Circumsphere Radius of Snub Cube?

The Circumsphere Radius of a Snub Cube is the radius of the sphere that contains the Snub Cube in such a way that all the vertices are lying on the sphere. It is an important geometric property of this Archimedean solid.

2. How Does the Calculator Work?

The calculator uses the Circumsphere Radius formula:

\[ R_c = \sqrt{\frac{3 - C}{4(2 - C)}} \times l_e \]

Where:

\( R_c \) — Circumsphere Radius of Snub Cube (m)
\( C \) — Tribonacci constant (1.839286755214161)
\( l_e \) — Edge Length of Snub Cube (m)

Explanation: The formula calculates the radius of the circumscribed sphere based on the edge length of the Snub Cube, using the mathematical constant known as the Tribonacci constant.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is crucial for understanding the spatial properties of the Snub Cube, its relationship with circumscribed spheres, and for applications in geometry, crystallography, and 3D modeling.

4. Using the Calculator

Tips: Enter the edge length of the Snub Cube in meters. The value must be positive and valid.

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 also known as the snub cuboctahedron.

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 when using the precise value of the Tribonacci constant and follows the established geometric formula.

Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula applies only to the Snub Cube. Other polyhedra have different formulas for their circumsphere radii.

Q5: What are practical applications of this calculation?
A: This calculation is used in mathematical research, computer graphics, architectural design, and anywhere precise geometric modeling of Snub Cubes is required.