1. What is the Edge Length of Icosidodecahedron?

The edge length of an icosidodecahedron is the measurement of any edge of this Archimedean solid. An icosidodecahedron is a polyhedron with 20 triangular faces and 12 pentagonal faces, all of equal edge length.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Volume \) — Volume of the icosidodecahedron (m³)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula derives from the mathematical relationship between the volume and edge length of a regular icosidodecahedron.

3. Importance of Edge Length Calculation

Details: Calculating the edge length from volume is essential in geometry, architecture, and material science where precise measurements of polyhedral structures are required.

4. Using the Calculator

Tips: Enter the volume of the icosidodecahedron in cubic meters. The value must be positive and greater than zero.

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), 30 identical vertices, and 60 edges of equal length.

Q2: Why is the formula specific to this shape?
A: The formula incorporates the mathematical constant √5, which appears in the geometry of pentagons and is fundamental to the icosidodecahedron's structure.

Q3: Can this calculator be used for irregular shapes?
A: No, this calculator only works for regular icosidodecahedrons where all edges are equal in length.

Q4: What are practical applications of this calculation?
A: This calculation is used in crystallography, architectural design, and the study of geometric properties of polyhedra.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact for perfect icosidodecahedrons, though real-world measurements may have slight variations.