Medium Edge Of Hexakis Octahedron Given Surface To Volume Ratio Calculator

Formula Used:

\[ \text{Medium Edge} = \frac{3}{14} \times (1 + 2\sqrt{2}) \times \frac{12 \times \sqrt{543 + 176\sqrt{2}}}{\text{Surface to Volume Ratio} \times \sqrt{6 \times (986 + 607\sqrt{2})}} \]

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 that helps define the shape and properties of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \text{Medium Edge} = \frac{3}{14} \times (1 + 2\sqrt{2}) \times \frac{12 \times \sqrt{543 + 176\sqrt{2}}}{\text{Surface to Volume Ratio} \times \sqrt{6 \times (986 + 607\sqrt{2})}} \]

Where:

\(\sqrt{}\) — Square root function
Surface to Volume Ratio — Ratio of total surface area to total volume of the Hexakis Octahedron

Explanation: This formula calculates the medium edge length based on the surface to volume ratio of the Hexakis Octahedron, incorporating various mathematical constants and operations.

3. Importance of Medium Edge Calculation

Details: Calculating the medium edge is crucial for understanding the geometric properties of Hexakis Octahedron, including its surface area, volume, and other dimensional characteristics. This information is valuable in fields such as crystallography, material science, and geometric modeling.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m (reciprocal 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 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, typically measured in square meters per cubic meter (1/m).

Q3: What are typical values for the medium edge?
A: The medium edge length varies depending on the specific dimensions of the Hexakis Octahedron and its surface to volume ratio. There is no fixed "normal" value as it depends on the particular instance of the polyhedron.

Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula and calculator are designed specifically for the Hexakis Octahedron and its medium edge calculation based on surface to volume ratio.

Q5: What precision can I expect from the calculation?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most geometric and engineering applications involving Hexakis Octahedra.