1. What is the Volume of Icosidodecahedron?

The volume of an icosidodecahedron is the total three-dimensional space enclosed by its surface. It's 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:

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

Explanation: This formula calculates the volume of an icosidodecahedron based on the radius of its circumscribed sphere.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is fundamental in mathematics, engineering, architecture, and various scientific fields where spatial measurements and properties are crucial.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is an icosidodecahedron?
A: An icosidodecahedron is an Archimedean solid with 32 faces (20 triangles and 12 pentagons), 60 edges, and 30 vertices.

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 is only applicable to the icosidodecahedron geometry.

Q4: What are the practical applications of this calculation?
A: This calculation is used in geometry, crystallography, architectural design, and various engineering applications involving polyhedral structures.

Q5: How accurate is the calculated volume?
A: The calculation is mathematically exact based on the input radius value and the geometric properties of the icosidodecahedron.