1. What is the Edge Length of Icosidodecahedron?

The edge length of an icosidodecahedron is the length of any of its edges. An icosidodecahedron is an Archimedean solid with 32 faces (20 triangles and 12 pentagons), 60 edges, and 30 vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge Length of Icosidodecahedron (m)
• \( r_c \) — Circumsphere Radius of Icosidodecahedron (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the edge length of an icosidodecahedron based on the radius of its circumscribed sphere, using the mathematical constant φ (phi) which is related to the golden ratio.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometry and properties of the icosidodecahedron, including its surface area, volume, and other dimensional characteristics in mathematical and architectural applications.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and valid. The calculator will compute the corresponding edge length of the icosidodecahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is an icosidodecahedron?
A: An icosidodecahedron is a convex polyhedron with 32 faces, 60 edges, and 30 vertices, consisting of 20 equilateral triangles and 12 regular pentagons.

Q2: What is the relationship between edge length and circumsphere radius?
A: The edge length is directly proportional to the circumsphere radius through the formula \( l_e = \frac{2 \times r_c}{1 + \sqrt{5}} \), which involves the golden ratio.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the icosidodecahedron. Other polyhedra have different relationships between edge length and circumsphere radius.

Q4: What are practical applications of this calculation?
A: This calculation is used in geometry, architecture, 3D modeling, and materials science where precise dimensional relationships of polyhedral structures are required.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using precise values. The accuracy of the result depends on the precision of the input circumsphere radius value.