Total Surface Area of Rhombicuboctahedron given Midsphere Radius Calculator

Formula Used:

\[ TSA = 2 \times (9 + \sqrt{3}) \times \left( \frac{2 \times r_m}{\sqrt{4 + 2 \times \sqrt{2}}} \right)^2 \]

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 Archimedean solid, which consists of 8 triangular and 18 square faces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 2 \times (9 + \sqrt{3}) \times \left( \frac{2 \times r_m}{\sqrt{4 + 2 \times \sqrt{2}}} \right)^2 \]

Where:

\( TSA \) — Total Surface Area of Rhombicuboctahedron (m²)
\( r_m \) — Midsphere Radius of Rhombicuboctahedron (m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)
\( \sqrt{2} \) — Square root of 2 (approximately 1.414)

Explanation: This formula calculates the total surface area based on the midsphere radius, which is the radius of the sphere tangent to all edges of the polyhedron.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of geometric solids is fundamental in various fields including architecture, materials science, and 3D modeling. It helps in determining material requirements, heat transfer properties, and structural characteristics.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombicuboctahedron?
A: A Rhombicuboctahedron is an Archimedean solid with 8 triangular faces and 18 square faces, totaling 26 faces, 24 vertices, and 48 edges.

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula is derived specifically for the Rhombicuboctahedron geometry.

Q4: What are practical applications of this calculation?
A: This calculation is useful in architectural design, crystal structure analysis, and mathematical modeling of complex geometric shapes.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using the precise formula, though computational rounding may introduce minor errors in decimal representation.