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.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge length of the rhombicosidodecahedron
• \( r_c \) — Circumsphere radius of the rhombicosidodecahedron

Explanation: This formula relates the edge length of a rhombicosidodecahedron to the radius of its circumscribed sphere through a mathematical constant derived from the geometry of this polyhedron.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for determining other geometric properties of the rhombicosidodecahedron, such as surface area, volume, and various other dimensional relationships in geometric modeling and architectural design.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and valid for accurate calculation of the edge length.

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 circumsphere radius?
A: The circumsphere radius is the radius of the sphere that passes through all the vertices of the polyhedron.

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: This calculation is used in architecture, 3D modeling, crystallography, and mathematical research involving polyhedral geometry.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, but practical accuracy depends on the precision of the input values and the computational capabilities.