Surface To Volume Ratio Of Hexakis Octahedron Given Medium Edge Calculator

Formula Used:

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

Surface to Volume Ratio:

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1. What is Surface to Volume Ratio of Hexakis Octahedron?

The Surface to Volume Ratio of a Hexakis Octahedron is a geometric property that represents the relationship between the total surface area and the total volume of this polyhedron. It indicates how much surface area is available per unit volume of the shape.

2. How Does the Calculator Work?

The calculator uses the following formula:

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

Where:

Medium Edge - The length of the medium edge of the Hexakis Octahedron (in meters)
\(\sqrt{}\) - Square root function

Explanation: This formula calculates the surface to volume ratio based on the geometric properties of the Hexakis Octahedron and its medium edge length.

3. Importance of Surface to Volume Ratio

Details: The surface to volume ratio is an important parameter in various fields including materials science, chemistry, and physics. It affects properties like heat transfer, reaction rates, and mechanical strength in polyhedral structures.

4. Using the Calculator

Tips: Enter the medium edge length of the Hexakis Octahedron in meters. The value must be positive and greater than zero.

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 faces, 72 edges, and 26 vertices.

Q2: What are the units of surface to volume ratio?
A: The surface to volume ratio is measured in reciprocal meters (m⁻¹), as it represents surface area per unit volume.

Q3: How does the medium edge affect the ratio?
A: The surface to volume ratio is inversely proportional to the medium edge length. As the edge length increases, the ratio decreases.

Q4: What are typical values for this ratio?
A: The ratio depends on the specific dimensions of the Hexakis Octahedron. For typical sizes, values range from fractions to several units of m⁻¹.

Q5: Where is this calculation used in practice?
A: This calculation is used in crystallography, nanotechnology, materials engineering, and geometric modeling where Hexakis Octahedron shapes are encountered.