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, a complex polyhedron with 48 faces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Long Edge — Length of the long edge (m)
• Medium Edge — Length of the medium edge (m)
• \(\sqrt{2}\) — Square root of 2 (approximately 1.4142)

Explanation: This formula establishes the proportional relationship between the medium and long edges of a Hexakis Octahedron based on its geometric properties.

3. Importance of Long Edge Calculation

Details: Calculating the long edge is essential for understanding the complete geometry of Hexakis Octahedron, which is important in crystallography, molecular modeling, and advanced geometric studies.

4. Using the Calculator

Tips: Enter the medium edge length in meters. The value must be positive and valid. The calculator will compute the corresponding long 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 cube. It has 48 faces, 72 edges, and 26 vertices.

Q2: Why is there a specific ratio between medium and long edges?
A: The ratio is derived from the geometric properties and symmetry of the Hexakis Octahedron, ensuring all faces remain congruent triangles.

Q3: Can this formula be used for any Hexakis Octahedron?
A: Yes, this formula applies to all regular Hexakis Octahedrons where all faces are congruent scalene triangles.

Q4: What are practical applications of this calculation?
A: This calculation is used in crystallography, architectural design, and mathematical modeling of complex polyhedra.

Q5: How accurate is this formula?
A: The formula is mathematically exact for perfect Hexakis Octahedrons and provides precise results when accurate inputs are given.