Surface To Volume Ratio Of Hexakis Octahedron Given Truncated Cuboctahedron Edge Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = \frac{12\sqrt{543 + 176\sqrt{2}}}{\sqrt{6(986 + 607\sqrt{2})}} \times \frac{7}{2\sqrt{60 + 6\sqrt{2}} \times l_e} \]

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 volume of this complex polyhedron. It is particularly important in materials science and chemistry where surface properties affect reactivity and other characteristics.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \text{Surface to Volume Ratio} = \frac{12\sqrt{543 + 176\sqrt{2}}}{\sqrt{6(986 + 607\sqrt{2})}} \times \frac{7}{2\sqrt{60 + 6\sqrt{2}} \times l_e} \]

Where:

\( l_e \) — Truncated Cuboctahedron Edge length (meters)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the surface to volume ratio based on the geometric properties of a Hexakis Octahedron derived from truncating a Cuboctahedron.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various scientific fields. Higher ratios indicate more surface area relative to volume, which is important for applications involving surface reactions, heat transfer, and material properties in nanotechnology and chemistry.

4. Using the Calculator

Tips: Enter the Truncated Cuboctahedron Edge length in meters. The value must be positive and greater than zero. The calculator will compute the surface to volume ratio in reciprocal meters (m⁻¹).

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 typical values for surface to volume ratio?
A: The ratio depends on the edge length. Smaller edge lengths result in higher surface to volume ratios, which is particularly significant at nanoscale dimensions.

Q3: Why is this calculation important in materials science?
A: Surface to volume ratio affects many material properties including reactivity, strength, thermal conductivity, and catalytic activity.

Q4: Can this calculator be used for microscopic particles?
A: Yes, the formula works at any scale as long as the edge length is provided in consistent units (typically meters).

Q5: Are there limitations to this calculation?
A: This calculation assumes a perfect geometric shape. Real-world materials may have surface imperfections that affect the actual surface to volume ratio.