1. What is the Volume of Rhombicosidodecahedron?

The volume of a Rhombicosidodecahedron is the total quantity of three dimensional space enclosed by the surface of this Archimedean solid. It's a complex polyhedron with 20 regular triangular faces, 30 square faces, and 12 regular pentagonal faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of Rhombicosidodecahedron (m³)
• \( r_c \) — Circumsphere Radius of Rhombicosidodecahedron (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the volume based on the circumsphere radius, using the mathematical properties of this specific polyhedron.

3. Importance of Volume Calculation

Details: Calculating the volume of complex polyhedra like the Rhombicosidodecahedron is important in geometry, architecture, material science, and various engineering applications where precise spatial measurements are required.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and valid. The calculator will compute the volume using the precise mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombicosidodecahedron?
A: It's an Archimedean solid with 62 faces (20 triangles, 30 squares, 12 pentagons), 120 edges, and 60 vertices.

Q2: Why is the formula so complex?
A: The complexity comes from the geometric relationships between the circumsphere radius and the various face dimensions of this highly symmetric polyhedron.

Q3: What units should I use?
A: Use consistent units (typically meters). The volume will be in cubic units of whatever unit you use for the radius.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Rhombicosidodecahedron. Other polyhedra have different volume formulas.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values and proper implementation of the formula.