1. What is Circumsphere Radius of Octahedron?

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

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumsphere Radius (m)
• \( TSA \) — Total Surface Area of Octahedron (m²)

Explanation: This formula derives from the relationship between the total surface area and the circumsphere radius of a regular octahedron, using mathematical constants and geometric properties.

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 octahedral structures.

4. Using the Calculator

Tips: Enter the total surface area of the octahedron in square meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular octahedron?
A: A regular octahedron is a polyhedron with 8 equilateral triangular faces, 12 edges, and 6 vertices.

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

Q3: Can this formula be used for irregular octahedrons?
A: No, this formula applies only to regular octahedrons where all faces are equilateral triangles.

Q4: What are practical applications of octahedron geometry?
A: Used in crystallography, molecular structures, architecture, and 3D computer graphics.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect regular octahedrons.