Medium Edge of Hexakis Octahedron given Volume Calculator

Formula Used:

\[ l_{medium} = \frac{3}{14} \times (1 + 2\sqrt{2}) \times \left( \frac{28V}{\sqrt{6(986 + 607\sqrt{2})}} \right)^{\frac{1}{3}} \]

Medium Edge of Hexakis Octahedron:

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1. What is Medium Edge of Hexakis Octahedron?

The Medium Edge of Hexakis Octahedron is the length of the medium edge of any of the congruent triangular faces of the Hexakis Octahedron. It is an important geometric parameter in this complex polyhedron structure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{medium} = \frac{3}{14} \times (1 + 2\sqrt{2}) \times \left( \frac{28V}{\sqrt{6(986 + 607\sqrt{2})}} \right)^{\frac{1}{3}} \]

Where:

\( l_{medium} \) — Medium Edge of Hexakis Octahedron (m)
\( V \) — Volume of Hexakis Octahedron (m³)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the medium edge length based on the volume of the Hexakis Octahedron, using mathematical constants and cube root operations.

3. Importance of Medium Edge Calculation

Details: Calculating the medium edge is crucial for understanding the geometric properties of Hexakis Octahedron, including surface area calculations, structural analysis, and various engineering applications involving this specific polyhedral shape.

4. Using the Calculator

Tips: Enter the volume of Hexakis Octahedron in cubic meters. The value must be positive and valid. The calculator will compute the corresponding medium 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: How is this formula derived?
A: The formula is derived from the geometric relationships between the volume and edge lengths of a Hexakis Octahedron, using mathematical constants specific to this polyhedron's structure.

Q3: What are the units for the result?
A: The result is in meters, matching the input volume units. Ensure consistent units for accurate calculations.

Q4: Are there limitations to this calculation?
A: This calculation assumes a perfect Hexakis Octahedron shape and may not account for manufacturing tolerances or deformations in real-world objects.

Q5: Can this calculator handle very large or very small volumes?
A: Yes, the calculator can handle a wide range of volume values, though extremely large or small values may be limited by computational precision.