Medium Edge of Hexakis Octahedron given Total Surface Area Calculator

Formula Used:

\[ \text{Medium Edge} = \frac{3}{14} \times (1 + 2\sqrt{2}) \times \sqrt{\frac{7 \times \text{Total Surface Area}}{3 \times \sqrt{543 + 176\sqrt{2}}}}} \]

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 an important geometric parameter in this complex polyhedron structure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Medium Edge} = \frac{3}{14} \times (1 + 2\sqrt{2}) \times \sqrt{\frac{7 \times \text{Total Surface Area}}{3 \times \sqrt{543 + 176\sqrt{2}}}}} \]

Where:

Total Surface Area - The total surface area of the Hexakis Octahedron in square meters
√ - Square root function

Explanation: This formula calculates the medium edge length based on the total surface area of the Hexakis Octahedron, using mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Medium Edge Calculation

Details: Calculating the medium edge is crucial for understanding the geometric properties of Hexakis Octahedron, architectural design applications, and mathematical modeling of complex polyhedral structures.

4. Using the Calculator

Tips: Enter the total surface area of the Hexakis Octahedron in square meters. The value must be positive and greater than zero for accurate 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 cuboctahedron. It has 48 congruent triangular faces, 72 edges, and 26 vertices.

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

Q3: What are the practical applications of this calculation?
A: This calculation is used in crystallography, architectural design, mathematical modeling, and in the study of polyhedral geometries.

Q4: What units should I use for the input?
A: Use consistent units for surface area (typically square meters), and the result will be in the corresponding linear units (meters).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the Hexakis Octahedron, assuming precise input values.