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 an important geometric property of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula calculates the short edge length based on the known medium edge length using the geometric relationships within the Hexakis Octahedron.

3. Importance of Short Edge Calculation

Details: Calculating the short edge is important for understanding the complete geometry of the Hexakis Octahedron, which has applications in crystallography, molecular modeling, and architectural design.

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

Q2: How many different edge lengths does a Hexakis Octahedron have?
A: A Hexakis Octahedron has three different edge lengths: short, medium, and long edges.

Q3: What are typical applications of Hexakis Octahedron calculations?
A: These calculations are used in crystallography, molecular modeling, architectural design, and mathematical research on polyhedra.

Q4: Can this formula be reversed to find medium edge from short edge?
A: Yes, the formula can be rearranged to solve for medium edge if the short edge is known.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, though practical accuracy depends on the precision of the input value and the implementation of the square root function.