1. What is Circumsphere Radius of Stellated Octahedron?

The Circumsphere Radius of a Stellated Octahedron is the radius of the sphere that contains the Stellated Octahedron in such a way that all the vertices are lying on the sphere. It represents the distance from the center of the polyhedron to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumsphere radius (m)
• \( l_e \) — Edge length of the stellated octahedron (m)
• \( \sqrt{6} \) — Square root of 6 (approximately 2.44949)

Explanation: The formula calculates the radius of the sphere that circumscribes the stellated octahedron based on its edge length.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important in geometry, 3D modeling, and material science for understanding the spatial dimensions and properties of stellated octahedrons in various applications.

4. Using the Calculator

Tips: Enter the edge length of the stellated octahedron in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a stellated octahedron?
A: A stellated octahedron is a polyhedron created by extending the faces of a regular octahedron until they meet again, forming a star-like shape with 24 faces.

Q2: How is the circumsphere radius different from the insphere radius?
A: The circumsphere radius touches all vertices of the polyhedron, while the insphere radius touches all faces from the inside.

Q3: Can this formula be used for regular octahedrons?
A: No, this specific formula applies only to stellated octahedrons. Regular octahedrons have a different circumsphere radius formula.

Q4: What are practical applications of stellated octahedrons?
A: Stellated octahedrons are used in architecture, crystal structures, molecular models, and as decorative elements in art and design.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using the precise formula, though practical measurements may have some margin of error.