1. What is Midsphere Radius of Cuboctahedron?

The Midsphere Radius of Cuboctahedron is the radius of the sphere which is tangent to every edge of the Cuboctahedron and also is present in between its insphere and the circumsphere.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_m \) — Midsphere Radius of Cuboctahedron (m)
• \( r_c \) — Circumsphere Radius of Cuboctahedron (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula provides a direct relationship between the circumsphere radius and midsphere radius of a cuboctahedron.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and 3D modeling for understanding the properties of cuboctahedrons and their spatial relationships.

4. Using the Calculator

Tips: Enter the circumsphere radius 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.

Q2: What is the relationship between midsphere and circumsphere radii?
A: The midsphere radius is exactly \( \frac{\sqrt{3}}{2} \) times the circumsphere radius for a cuboctahedron.

Q3: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to cuboctahedrons. Other polyhedrons have different relationships between their midsphere and circumsphere radii.

Q4: What are practical applications of this calculation?
A: This calculation is used in crystallography, molecular modeling, architecture, and geometric design.

Q5: How accurate is this formula?
A: The formula is mathematically exact for perfect cuboctahedrons.