1. What is the Edge Length of Icosahedron?

The edge length of an icosahedron is the length of any of the 30 edges of this regular polyhedron. An icosahedron has 20 equilateral triangular faces, 12 vertices, and 30 edges.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Circumsphere\ Radius \) — Radius of the sphere that contains all vertices of the icosahedron (m)
• \( \sqrt{} \) — Square root function

Explanation: This formula establishes the mathematical relationship between the circumsphere radius and the edge length of a regular icosahedron.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for various geometric applications, including volume and surface area calculations, architectural design, and 3D modeling of icosahedral structures.

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 a regular icosahedron?
A: A regular icosahedron is a convex polyhedron with 20 identical equilateral triangular faces, 12 vertices, and 30 edges.

Q2: How many edges does an icosahedron have?
A: A regular icosahedron has exactly 30 edges of equal length.

Q3: What is the circumsphere radius?
A: The circumsphere radius is the radius of the sphere that passes through all vertices of the icosahedron.

Q4: Can this formula be used for irregular icosahedrons?
A: No, this formula applies only to regular icosahedrons where all edges are equal and all faces are equilateral triangles.

Q5: What are some real-world applications of icosahedrons?
A: Icosahedrons are used in architecture, geodesic domes, molecular structures (like viruses), and various mathematical models.