Surface to Volume Ratio of Hexakis Icosahedron given Total Surface Area Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = \frac{6}{5} \times \sqrt{\frac{10 \times (417 + 107 \times \sqrt{5})}{6 \times (185 + 82 \times \sqrt{5})}} \times \sqrt{\frac{15 \times \sqrt{10 \times (417 + 107 \times \sqrt{5})}}{44 \times \text{Total Surface Area}}} \]

Surface to Volume Ratio:

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

The Surface to Volume Ratio of a Hexakis Icosahedron represents the relationship between its total surface area and its volume. It indicates how much surface area is available per unit volume of the polyhedron, which is important in various geometric and physical applications.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)
Total Surface Area — The total surface area of the Hexakis Icosahedron in square meters

Explanation: The formula calculates the surface to volume ratio based on the geometric properties of the Hexakis Icosahedron and its given total surface area.

3. Importance of Surface to Volume Ratio

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 total surface area of the Hexakis Icosahedron in square meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Hexakis Icosahedron?
A: A Hexakis Icosahedron is a Catalan solid that is the dual of the truncated dodecahedron. It has 120 faces, 180 edges, and 62 vertices.

Q2: Why is the surface to volume ratio important?
A: It helps understand how the surface area scales with volume, which is important for predicting physical and chemical properties of materials.

Q3: What units should I use for the total surface area?
A: The calculator uses square meters (m²) for surface area input, and returns the ratio in meters⁻¹ (m⁻¹).

Q4: Can this calculator handle very large or very small values?
A: Yes, the calculator can handle a wide range of values, but extremely large or small numbers may affect precision.

Q5: Is this formula specific to Hexakis Icosahedron?
A: Yes, this formula is specifically derived for calculating the surface to volume ratio of a Hexakis Icosahedron given its total surface area.