1. What is the Circumsphere Radius of Cuboctahedron?

The Circumsphere Radius of Cuboctahedron is the radius of the sphere that contains the Cuboctahedron in such a way that all the vertices are lying on the sphere. It is a fundamental geometric property of this Archimedean solid.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumsphere Radius of Cuboctahedron (m)
• \( l_e \) — Edge Length of Cuboctahedron (m)

Explanation: The circumsphere radius is equal to the edge length in a cuboctahedron, making the calculation straightforward.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important in geometry, crystallography, and materials science for understanding the spatial arrangement and packing efficiency of cuboctahedral structures.

4. Using the Calculator

Tips: Enter the edge length of the cuboctahedron in meters. The value must be positive and valid.

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 12 identical vertices and 24 edges.

Q2: Why is the circumsphere radius equal to the edge length?
A: Due to the symmetric geometry of the cuboctahedron, the distance from the center to any vertex equals the edge length.

Q3: What are the applications of cuboctahedrons?
A: Cuboctahedrons are used in crystallography, nanotechnology, and architectural design due to their efficient packing properties.

Q4: Can this formula be used for other polyhedrons?
A: No, this specific relationship only applies to cuboctahedrons. Other polyhedrons have different circumsphere radius formulas.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect cuboctahedrons, as it's derived from geometric principles.