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 of equal length.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Lateral Surface Area — The total area of all lateral faces of the icosahedron (in m²)
• √ — Square root function

Explanation: This formula derives from the geometric properties of a regular icosahedron, relating the lateral surface area to the edge length through mathematical constants.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for various geometric computations, including volume calculation, surface area determination, and understanding the spatial properties of the icosahedron in 3D modeling and mathematical applications.

4. Using the Calculator

Tips: Enter the lateral surface area of the icosahedron in square 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 of equal length.

Q2: How many faces does an icosahedron have?
A: An icosahedron has 20 triangular faces, all of which are equilateral triangles.

Q3: What is the relationship between edge length and lateral surface area?
A: The lateral surface area is proportional to the square of the edge length, following the formula: LSA = (9√3/2) × edge_length²

Q4: Can this calculator be used for irregular icosahedrons?
A: No, this calculator is specifically designed for regular icosahedrons where all edges are of equal length and all faces are equilateral triangles.

Q5: What are some real-world applications of icosahedrons?
A: Icosahedrons are used in architecture, molecular modeling (such as viral capsids), geodesic domes, and various mathematical and geometric studies.