1. What is the Midsphere Radius of Triakis Octahedron?

The Midsphere Radius of Triakis Octahedron is the radius of the sphere for which all the edges of the Triakis Octahedron become a tangent line on that sphere. It represents the sphere that is tangent to all edges of the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_m \) — Midsphere Radius of Triakis Octahedron (m)
• \( l_{e(Octahedron)} \) — Octahedral Edge Length of Triakis Octahedron (m)

Explanation: The midsphere radius is exactly half the length of the octahedral edge of the Triakis Octahedron.

3. Importance of Midsphere Radius Calculation

Details: Calculating the midsphere radius is important in geometry and 3D modeling for understanding the spatial properties of the Triakis Octahedron and its relationship with inscribed spheres.

4. Using the Calculator

Tips: Enter the octahedral edge length of the Triakis Octahedron in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Octahedron?
A: A Triakis Octahedron is a Catalan solid that is the dual of the truncated cube. It has 24 isosceles triangular faces.

Q2: How is the midsphere different from the insphere?
A: The midsphere is tangent to all edges of the polyhedron, while the insphere is tangent to all faces.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Triakis Octahedron. Other polyhedra have different relationships between edge length and midsphere radius.

Q4: What are practical applications of this calculation?
A: This calculation is used in crystallography, molecular modeling, and architectural design where Triakis Octahedron shapes appear.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect Triakis Octahedron shape.