1. What is the Total Surface Area of Rhombicosidodecahedron?

The Rhombicosidodecahedron is an Archimedean solid with 20 regular triangular faces, 30 square faces, and 12 regular pentagonal faces. The total surface area represents the sum of the areas of all these faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( TSA \) — Total Surface Area of Rhombicosidodecahedron (m²)
• \( r_m \) — Midsphere Radius of Rhombicosidodecahedron (m)
• \( \sqrt{} \) — Square root function

Explanation: This formula calculates the total surface area based on the midsphere radius, incorporating the geometric properties of the Rhombicosidodecahedron.

3. Importance of Surface Area Calculation

Details: Calculating the surface area is crucial for various applications including material estimation, thermal properties analysis, and understanding the geometric characteristics of this complex polyhedron.

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 Rhombicosidodecahedron?
A: It's one of the 13 Archimedean solids, featuring a combination of triangular, square, and pentagonal faces in a highly symmetric arrangement.

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

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Rhombicosidodecahedron due to its unique geometric properties.

Q4: What are practical applications of this calculation?
A: Applications include architectural design, material science, 3D modeling, and mathematical research involving polyhedral geometry.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the given formula, though computational precision depends on the implementation.