1. What is the Insphere Radius of Hexakis Octahedron?

The Insphere Radius of Hexakis Octahedron is defined as the radius of the sphere that is contained by the Hexakis Octahedron in such a way that all the faces just touch the sphere. It represents the largest sphere that can fit inside the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Insphere Radius of Hexakis Octahedron (m)
• \( r_m \) — Midsphere Radius of Hexakis Octahedron (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: The formula calculates the insphere radius based on the given midsphere radius, using geometric relationships specific to the Hexakis Octahedron.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and material science for understanding the internal space and packing properties of polyhedral structures.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Hexakis Octahedron?
A: A Hexakis Octahedron is a Catalan solid that is the dual of the truncated cuboctahedron, with 48 faces, 72 edges, and 26 vertices.

Q2: How is the insphere radius different from the midsphere radius?
A: The insphere radius is the radius of the largest sphere that fits inside the polyhedron, while the midsphere radius is the radius of the sphere that touches all edges.

Q3: What are typical values for the insphere radius?
A: The insphere radius depends on the size of the Hexakis Octahedron and is typically proportional to the midsphere radius.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula is derived for the Hexakis Octahedron only. Other polyhedra have different geometric relationships.

Q5: What precision should I expect from the calculation?
A: The calculator provides results with up to 10 decimal places for high precision in geometric calculations.