Surface To Volume Ratio Of Hexakis Octahedron Given Short Edge Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = \frac{12\sqrt{543+176\sqrt{2}}}{\sqrt{6(986+607\sqrt{2})}} \times \frac{10-\sqrt{2}}{14 \times \text{Short Edge}} \]

Surface to Volume Ratio:

Unit Converter ▲

Unit Converter ▼

From:	To:

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

The Surface to Volume Ratio of a Hexakis Octahedron is a measure that compares the total surface area to the total volume of this complex polyhedron. It's an important geometric property that indicates how much surface area is available per unit volume.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \text{Surface to Volume Ratio} = \frac{12\sqrt{543+176\sqrt{2}}}{\sqrt{6(986+607\sqrt{2})}} \times \frac{10-\sqrt{2}}{14 \times \text{Short Edge}} \]

Where:

Short Edge — Length of the shortest edge of the Hexakis Octahedron (in meters)
√2 — Square root of 2 (approximately 1.4142)

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

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 affects properties like diffusion rates, heat transfer, and chemical reactivity in materials with this geometric structure.

4. Using the Calculator

Tips: Enter the length of the short edge 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 cube. It has 48 faces, 72 edges, and 26 vertices.

Q2: Why is the surface to volume ratio important?
A: This ratio is critical in determining how materials interact with their environment, affecting properties like dissolution rates, catalytic activity, and thermal properties.

Q3: What units should I use for the short edge measurement?
A: The calculator uses meters as the default unit, but the ratio calculation is consistent as long as you use the same unit system throughout.

Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for the Hexakis Octahedron geometry.

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.