1. What is Edge Length of Icosidodecahedron?

The edge length of an icosidodecahedron is the length of any edge of this Archimedean solid, which has 20 triangular faces and 12 pentagonal faces. It is a key geometric parameter for various calculations involving this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge Length of Icosidodecahedron (m)
• \( P_{Triangle} \) — Triangular Face Perimeter of Icosidodecahedron (m)

Explanation: Since each triangular face of an icosidodecahedron is equilateral, the perimeter is simply 3 times the edge length. This formula reverses that relationship to find the edge length from the perimeter.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is fundamental for determining other properties of the icosidodecahedron, such as surface area, volume, and various geometric relationships between its faces and vertices.

4. Using the Calculator

Tips: Enter the triangular face perimeter 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: Why is the triangular face perimeter divided by 3?
A: Because each triangular face is equilateral, meaning all three sides are equal in length. Dividing the perimeter by 3 gives the length of one side (edge).

Q3: Can this formula be used for other polyhedra?
A: This specific formula applies only to icosidodecahedrons and other polyhedra with equilateral triangular faces.

Q4: What are the units of measurement?
A: The calculator uses meters, but the formula works with any consistent unit of length (cm, mm, inches, etc.).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, assuming the input perimeter is accurate and the triangular faces are perfectly equilateral.