1. What is the Short Edge of Hexakis Octahedron?

The Short Edge of Hexakis Octahedron is the length of the shortest edge of any of the congruent triangular faces of the Hexakis Octahedron. It is a key geometric parameter in this polyhedron structure.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula establishes a precise mathematical relationship between the short and long edges of a Hexakis Octahedron.

3. Importance of Short Edge Calculation

Details: Calculating the short edge is essential for geometric analysis, structural design, and mathematical modeling of Hexakis Octahedron shapes in various applications.

4. Using the Calculator

Tips: Enter the long edge value in meters. The value must be positive and valid. The calculator will compute the corresponding short 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 the square root of 2 used in this formula?
A: The square root of 2 appears naturally in geometric relationships involving right angles and is fundamental to many polyhedral calculations.

Q3: What are typical applications of this calculation?
A: This calculation is used in crystallography, architectural design, mathematical modeling, and geometric analysis of polyhedral structures.

Q4: How accurate is this formula?
A: The formula is mathematically exact for a perfect Hexakis Octahedron and provides precise results when accurate input values are used.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit, but the result can be converted to other units as needed since the relationship is proportional.