1. What is the Midsphere Radius of Octahedron?

The Midsphere Radius of an Octahedron is the radius of the sphere that is tangent to all the edges of the Octahedron. It lies midway between the insphere (tangent to faces) and circumsphere (passing through vertices).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_m \) — Midsphere Radius of Octahedron (m)
• \( r_i \) — Insphere Radius of Octahedron (m)

Explanation: The formula establishes a direct mathematical relationship between the midsphere radius and insphere radius of a regular octahedron, using the constant factor \( \sqrt{\frac{3}{2}} \).

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and 3D modeling for understanding the spatial properties of octahedrons and their relationship with tangent spheres.

4. Using the Calculator

Tips: Enter the insphere radius value in 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 does the midsphere differ from the insphere?
A: The insphere is tangent to all faces of the octahedron, while the midsphere is tangent to all edges 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 this calculation?
A: This calculation is used in crystallography, molecular modeling, architectural design, and computer graphics where octahedral structures are involved.

Q5: How accurate is this formula?
A: The formula is mathematically exact for regular octahedrons and provides precise results when correct input values are used.