Surface to Volume Ratio of Hexakis Octahedron Calculator

Surface to Volume Ratio of Hexakis Octahedron Formula:

\[ \text{RA/V} = \frac{12 \times \sqrt{543 + (176 \times \sqrt{2})}}{\text{Long Edge of Hexakis Octahedron} \times \sqrt{6 \times (986 + (607 \times \sqrt{2}))}} \]

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 represents the relationship between its total surface area and total volume. It's an important geometric property that indicates how much surface area is available per unit volume of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{RA/V} = \frac{12 \times \sqrt{543 + (176 \times \sqrt{2})}}{\text{Long Edge} \times \sqrt{6 \times (986 + (607 \times \sqrt{2}))}} \]

Where:

\( \text{RA/V} \) — Surface to Volume Ratio (m⁻¹)
\( \text{Long Edge} \) — Length of the long edge of the Hexakis Octahedron (m)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the ratio of surface area to volume based on the geometric properties of the Hexakis Octahedron, specifically using the length of its long edge.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and physics. It helps determine properties like reactivity, heat transfer efficiency, and diffusion rates in polyhedral structures.

4. Using the Calculator

Tips: Enter the length of the long edge of the Hexakis Octahedron in 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: Why is surface to volume ratio important?
A: It indicates how much surface area is available relative to the volume, which affects properties like chemical reactivity, heat dissipation, and mass transfer.

Q3: What units are used in this calculation?
A: The long edge is measured in meters (m) and the surface to volume ratio is expressed in inverse meters (m⁻¹).

Q4: Can this calculator handle very small or large values?
A: Yes, as long as the input value is positive and within reasonable computational limits.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the given formula, though computational precision may introduce minor rounding errors.