1. What is Midsphere Radius of Hexakis Octahedron?

The Midsphere Radius of Hexakis Octahedron is defined as the radius of the sphere for which all the edges of the Hexakis 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 (m)
• \( l_e \) — Truncated Cuboctahedron Edge length (m)
• \( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

3. Formula Explanation

Details: This formula calculates the midsphere radius of a Hexakis Octahedron based on the length of its truncated cuboctahedron edge. The formula incorporates mathematical constants and geometric relationships specific to this polyhedron structure.

4. Using the Calculator

Tips: Enter the truncated cuboctahedron edge length in meters. The value must be positive and greater than zero. The calculator will compute the corresponding midsphere radius.

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. It has 48 faces, 72 edges, and 26 vertices.

Q2: What is the significance of midsphere radius?
A: The midsphere radius is important in geometry as it represents the sphere that is tangent to all edges of the polyhedron, providing insight into the polyhedron's spatial properties.

Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to Hexakis Octahedra and their relationship with truncated cuboctahedron edges.

Q4: What units should be used?
A: The calculator uses meters for both input and output, but any consistent unit system can be used as long as it's applied consistently.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact based on the input value, with results rounded to 6 decimal places for practical use.