1. What is the Edge Length of Rhombicosidodecahedron?

The Edge Length of a Rhombicosidodecahedron is the length of any edge of this Archimedean solid. It is a fundamental geometric property used in various mathematical and engineering calculations involving this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge Length of Rhombicosidodecahedron (m)
• \( r_m \) — Midsphere Radius of Rhombicosidodecahedron (m)

Explanation: This formula calculates the edge length from the midsphere radius using the geometric properties of the Rhombicosidodecahedron.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for determining other geometric properties, surface area, volume, and for applications in architecture, design, and mathematical modeling of polyhedra.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombicosidodecahedron?
A: A Rhombicosidodecahedron is an Archimedean solid with 20 regular triangular faces, 30 square faces, and 12 regular pentagonal faces.

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: What are typical values for edge length?
A: The edge length depends on the size of the polyhedron. For standard units, it typically ranges from centimeters to meters depending on the application.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Rhombicosidodecahedron due to its unique geometric properties.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the Rhombicosidodecahedron.