Total Surface Area of Snub Cube given Circumsphere Radius Calculator

Formula Used:

\[ TSA = 2 \times (3 + 4 \times \sqrt{3}) \times \left( \frac{rc}{\sqrt{\frac{3 - C}{4 \times (2 - C)}}} \right)^2 \]

Total Surface Area of Snub Cube:

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1. What is the Total Surface Area of Snub Cube?

The Total Surface Area of a Snub Cube is the total quantity of plane enclosed by the entire surface of this Archimedean solid. It represents the sum of all the areas of its faces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 2 \times (3 + 4 \times \sqrt{3}) \times \left( \frac{rc}{\sqrt{\frac{3 - C}{4 \times (2 - C)}}} \right)^2 \]

Where:

\( TSA \) — Total Surface Area of Snub Cube (m²)
\( rc \) — Circumsphere Radius of Snub Cube (m)
\( C \) — Tribonacci constant (1.839286755214161)
\( \sqrt{3} \) — Square root of 3 (approximately 1.73205080757)

Explanation: This formula calculates the total surface area based on the circumsphere radius, using the mathematical properties of the Snub Cube and the Tribonacci constant.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of geometric solids is fundamental in mathematics, engineering, and architecture. For the Snub Cube, this calculation helps understand its geometric properties and applications in various fields.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and greater than 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 equilateral triangles.

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 practical applications of this calculation?
A: This calculation is used in mathematical research, 3D modeling, architectural design, and understanding geometric properties of complex polyhedra.

Q4: How accurate is this formula?
A: The formula is mathematically exact for a perfect Snub Cube with the given circumsphere radius.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the base unit. For other units, convert your measurement to meters before calculation.