1. What is the Circumsphere Radius of Cuboctahedron?

The Circumsphere Radius of a 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 represents the distance from the center of the Cuboctahedron to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumsphere Radius of Cuboctahedron (m)
• \( P \) — Perimeter of Cuboctahedron (m)

Explanation: This formula provides a direct relationship between the perimeter of the Cuboctahedron and its circumsphere radius, with a constant divisor of 24.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important in geometry and 3D modeling for understanding the spatial properties of the Cuboctahedron and its relationship with circumscribed spheres.

4. Using the Calculator

Tips: Enter the perimeter of the Cuboctahedron in meters. The value must be valid (perimeter > 0).

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 identical edges.

Q2: Why is the divisor 24 in the formula?
A: The divisor 24 comes from the geometric properties of the Cuboctahedron, specifically relating its perimeter to its circumsphere radius through mathematical derivation.

Q3: What are the units for the circumsphere radius?
A: The circumsphere radius is measured in the same units as the perimeter input (typically meters).

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to Cuboctahedrons as it's derived from their unique geometric properties.

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