Surface To Volume Ratio Of Triakis Icosahedron Given Pyramidal Edge Length Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = \frac{12\sqrt{109 - 30\sqrt{5}}}{5 + 7\sqrt{5}} \times \frac{15 - \sqrt{5}}{22 \times \text{Pyramidal Edge Length}} \]

Surface to Volume Ratio:

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

The Surface to Volume Ratio of a Triakis Icosahedron 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 mathematical formula:

\[ \text{Surface to Volume Ratio} = \frac{12\sqrt{109 - 30\sqrt{5}}}{5 + 7\sqrt{5}} \times \frac{15 - \sqrt{5}}{22 \times \text{Pyramidal Edge Length}} \]

Where:

\(\sqrt{}\) — Square root function
Pyramidal Edge Length — Length of the line connecting any two adjacent vertices of pyramid of Triakis Icosahedron (in meters)

Explanation: The formula calculates the ratio by considering the geometric properties of the Triakis Icosahedron and its pyramidal edge length.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is important in various fields including materials science, chemistry, and physics. It helps understand properties like diffusion rates, heat transfer, and reaction kinetics in geometric structures.

4. Using the Calculator

Tips: Enter the pyramidal edge length in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Triakis Icosahedron?
A: A Triakis Icosahedron is a Catalan solid that is the dual of the truncated dodecahedron. It has 60 faces, 90 edges, and 32 vertices.

Q2: What units are used for the 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 pyramidal edge length affect the ratio?
A: The surface to volume ratio is inversely proportional to the pyramidal 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 Triakis Icosahedron. For standard sizes, values typically range based on the pyramidal edge length.

Q5: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for the Triakis Icosahedron. Other polyhedra have different formulas for calculating surface to volume ratios.