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)
• \( V \) — Volume of Octahedron (m³)

Explanation: This formula derives the circumsphere radius from the volume of a regular octahedron using mathematical relationships between the geometric properties.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important in geometry, 3D modeling, and various engineering applications where understanding the spatial dimensions and relationships of octahedral structures is required.

4. Using the Calculator

Tips: Enter the volume of the octahedron in cubic meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular octahedron?
A: A regular octahedron is a polyhedron with 8 equilateral triangular faces, 6 vertices, and 12 edges. It is one of the five Platonic solids.

Q2: How is the circumsphere different from the insphere?
A: The circumsphere passes through all vertices of the octahedron, while the insphere is tangent to all faces of the octahedron.

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

Q4: What are practical applications of octahedrons?
A: Octahedrons are used in crystallography (diamond crystal structure), molecular geometry, architecture, and various engineering designs.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular octahedrons, provided the input volume is accurate.