1. What is 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 touches the midpoints of all edges of the polyhedron.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( r_m \) — Midsphere Radius of Triakis Octahedron (m)
• \( TSA \) — Total Surface Area of Triakis Octahedron (m²)

Explanation: This formula derives the midsphere radius from the total surface area using geometric relationships specific to the Triakis Octahedron structure.

3. Importance of Midsphere Radius Calculation

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

4. Using the Calculator

Tips: Enter the total surface area of the Triakis Octahedron in square meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Octahedron?
A: A Triakis Octahedron is a Catalan solid that can be obtained by adding a square pyramid on each face of a regular octahedron.

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

Q3: What are the applications of this calculation?
A: This calculation is used in crystallography, molecular modeling, and architectural design involving polyhedral structures.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to Triakis Octahedron as it incorporates geometric constants unique to this shape.

Q5: What units should be used for input?
A: The calculator expects total surface area in square meters and returns midsphere radius in meters.