1. What is Edge Length of Cuboctahedron given Perimeter?

The edge length of a cuboctahedron given its perimeter is calculated by dividing the total perimeter by 24, as a cuboctahedron has 24 edges of equal length.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge Length of Cuboctahedron (m)
• \( P \) — Perimeter of Cuboctahedron (m)

Explanation: Since a cuboctahedron has 24 equal edges, the edge length is simply the total perimeter divided by 24.

3. Importance of Edge Length Calculation

Details: Calculating the edge length from perimeter is essential in geometry and materials science for determining the dimensions of cuboctahedral structures and understanding their properties.

4. Using the Calculator

Tips: Enter the perimeter of the cuboctahedron in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a cuboctahedron?
A: A cuboctahedron is an Archimedean solid with 8 triangular faces and 6 square faces, having 24 identical edges.

Q2: Why divide by 24?
A: A cuboctahedron has exactly 24 edges of equal length, so dividing the total perimeter by 24 gives the length of one edge.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to cuboctahedra. Other polyhedra have different numbers of edges and edge length relationships.

Q4: What are typical applications of this calculation?
A: This calculation is used in crystallography, nanotechnology, and architectural design where cuboctahedral structures are employed.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect cuboctahedra with all edges of equal length.