Total Surface Area of Rhombicuboctahedron Calculator

Total Surface Area of Rhombicuboctahedron Formula:

\[ TSA = 2 \times (9 + \sqrt{3}) \times le^2 \]

Total Surface Area of Rhombicuboctahedron:

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1. What is the Total Surface Area of Rhombicuboctahedron?

The Total Surface Area of a Rhombicuboctahedron is the total quantity of plane enclosed by the entire surface of this polyhedron. A Rhombicuboctahedron is an Archimedean solid with 8 triangular and 18 square faces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 2 \times (9 + \sqrt{3}) \times le^2 \]

Where:

\( TSA \) — Total Surface Area of Rhombicuboctahedron (m²)
\( le \) — Edge Length of Rhombicuboctahedron (m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula calculates the total surface area by summing the areas of all 26 faces (8 equilateral triangles and 18 squares) of the Rhombicuboctahedron.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of polyhedra is important in geometry, architecture, material science, and various engineering applications where surface properties affect performance and functionality.

4. Using the Calculator

Tips: Enter the edge length in meters. The value must be positive and valid. The calculator will compute the total surface area using the standard formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombicuboctahedron?
A: A Rhombicuboctahedron is an Archimedean solid with 26 faces: 8 equilateral triangles and 18 squares, 24 identical vertices, and 48 edges.

Q2: Why is the formula structured this way?
A: The formula accounts for the combined area of all triangular and square faces, with the constant (9 + √3) derived from the geometry of the polyhedron.

Q3: Can this formula be used for any polyhedron?
A: No, this specific formula applies only to the Rhombicuboctahedron. Different polyhedra have different surface area formulas.

Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, crystallography, 3D modeling, and any field dealing with polyhedral structures.

Q5: How accurate is this formula?
A: The formula is mathematically exact for a perfect Rhombicuboctahedron and provides precise results when accurate edge length measurements are used.