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 an important geometric measurement in this complex polyhedron structure.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• Surface to Volume Ratio - The ratio of surface area to volume of the Hexakis Octahedron (m⁻¹)

Explanation: This formula calculates the long edge length based on the surface to volume ratio of the Hexakis Octahedron, using mathematical constants derived from the geometry of this specific polyhedron.

3. Importance of Long Edge Calculation

Details: Calculating the long edge of a Hexakis Octahedron is crucial for geometric analysis, architectural design, and understanding the spatial properties of this complex polyhedral structure.

4. Using the Calculator

Tips: Enter the surface to volume ratio in m⁻¹. The value must be greater than zero for valid calculation.

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: How is the surface to volume ratio measured?
A: The surface to volume ratio is calculated by dividing the total surface area by the total volume of the Hexakis Octahedron.

Q3: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the size and proportions of the specific Hexakis Octahedron, with smaller structures having higher ratios.

Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for Hexakis Octahedrons due to their unique geometric properties.

Q5: What units should I use for the result?
A: The result is in meters, but you can convert it to other length units as needed for your application.