1. What is the Long Edge of Hexakis Octahedron?

The Long Edge of Hexakis Octahedron is the length of the long edge of any of the congruent triangular faces of the Hexakis Octahedron. It is a geometric property that relates to the overall dimensions and proportions of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Long Edge — Length of the long edge of Hexakis Octahedron (m)
• Short Edge — Length of the short edge of Hexakis Octahedron (m)
• \(\sqrt{2}\) — Square root of 2 (approximately 1.4142)

Explanation: This formula establishes a precise mathematical relationship between the long and short edges of a Hexakis Octahedron, derived from its geometric properties.

3. Importance of Long Edge Calculation

Details: Calculating the long edge is essential for understanding the complete geometry of the Hexakis Octahedron, which is important in various fields including crystallography, architecture, and mathematical modeling of polyhedral structures.

4. Using the Calculator

Tips: Enter the short edge length in meters. The value must be positive and valid. The calculator will compute the corresponding long edge length using the established mathematical relationship.

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

Q2: Why is there a specific formula for this calculation?
A: The formula is derived from the precise geometric relationships and symmetry properties inherent to the Hexakis Octahedron structure.

Q3: Can this formula be used for any size of Hexakis Octahedron?
A: Yes, the formula is scalable and applies to Hexakis Octahedrons of any size, as it represents a proportional relationship between edges.

Q4: What are the practical applications of this calculation?
A: This calculation is useful in geometric modeling, 3D design, architectural planning, and mathematical research involving polyhedral structures.

Q5: How accurate is this formula?
A: The formula is mathematically exact for a perfect Hexakis Octahedron, providing precise results when correct input values are used.