Medium Edge of Hexakis Octahedron Calculator

Medium Edge of Hexakis Octahedron Formula:

\[ le(Medium) = \frac{3}{14} \times (1 + 2 \times \sqrt{2}) \times le(Long) \]

Medium Edge of Hexakis Octahedron:

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1. What is the 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 a geometric property that helps define the shape and dimensions of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ le(Medium) = \frac{3}{14} \times (1 + 2 \times \sqrt{2}) \times le(Long) \]

Where:

\( le(Medium) \) — Medium Edge of Hexakis Octahedron (m)
\( le(Long) \) — Long Edge of Hexakis Octahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: The formula calculates the medium edge length based on the known long edge length using a constant ratio derived from the geometric properties of the Hexakis Octahedron.

3. Importance of Medium Edge Calculation

Details: Calculating the medium edge is essential for understanding the complete geometry of the Hexakis Octahedron, which is important in various fields including crystallography, architecture, and mathematical modeling of complex polyhedra.

4. Using the Calculator

Tips: Enter the long edge length in 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: Why is the square root of 2 used in the formula?
A: The square root of 2 appears naturally in geometric calculations involving right angles and is fundamental to the proportions of the Hexakis Octahedron.

Q3: Can this formula be used for any Hexakis Octahedron?
A: Yes, this formula applies to all regular Hexakis Octahedrons as it's derived from their fundamental geometric properties.

Q4: What are the practical applications of this calculation?
A: This calculation is useful in crystallography for determining crystal structures, in architecture for designing complex geometric shapes, and in 3D modeling for creating accurate representations.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using precise values. The accuracy of the result depends on the precision of the input value and the computational precision of the calculator.