1. What is the Long Edge of Hexakis Octahedron?

The Long Edge of Hexakis Octahedron is the length of the longest edge of any of the congruent triangular faces of the Hexakis Octahedron, a Catalan solid that is the dual of the truncated cuboctahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Volume \) — Volume of the Hexakis Octahedron (m³)

Explanation: This formula calculates the long edge length based on the volume of the polyhedron, using the mathematical relationship specific to the Hexakis Octahedron's geometry.

3. Importance of Long Edge Calculation

Details: Calculating the long edge is essential for understanding the dimensions and proportions of the Hexakis Octahedron, which is important in geometry, crystallography, and architectural design applications.

4. Using the Calculator

Tips: Enter the volume of the Hexakis Octahedron in cubic meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

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

Q2: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect Hexakis Octahedron, assuming precise volume measurement.

Q3: Can this formula be used for other polyhedra?
A: No, this formula is specific to the Hexakis Octahedron. Other polyhedra have different formulas relating volume to edge lengths.

Q4: What are practical applications of this calculation?
A: This calculation is useful in crystallography, molecular modeling, architectural design, and mathematical education.

Q5: How is the volume typically measured for real objects?
A: For physical objects, volume can be measured through displacement methods or calculated from other known dimensions using appropriate formulas.