1. What is Truncated Cuboctahedron Edge of Hexakis Octahedron?

The Truncated Cuboctahedron Edge of Hexakis Octahedron is the length of the edges of a Hexakis Octahedron that is created by truncating the vertices of a Cuboctahedron. It represents a specific geometric measurement in polyhedral geometry.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• Insphere Radius - The radius of the sphere contained by the Hexakis Octahedron
• \(\sqrt{}\) - Square root function

Explanation: This formula calculates the edge length based on the insphere radius using specific mathematical constants and operations.

3. Importance of This Calculation

Details: This calculation is important in geometric modeling, architectural design, and mathematical research involving polyhedral structures. It helps in understanding the relationship between different geometric properties of complex polyhedra.

4. Using the Calculator

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

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, featuring 48 faces.

Q2: What units should I use for the input?
A: The calculator uses meters as the unit of measurement. Ensure consistent units for accurate results.

Q3: Can this calculator handle very small or very large values?
A: The calculator can handle a wide range of values, but extremely small values may be limited by floating-point precision.

Q4: What is the significance of the mathematical constants in the formula?
A: The constants (402, 195, 194, 60, 6, etc.) are derived from the geometric properties and relationships within the polyhedral structure.

Q5: Are there any limitations to this calculation?
A: The calculation assumes perfect geometric shapes and may not account for real-world imperfections or variations.