Icosahedral Edge Length of Triakis Icosahedron given Surface to Volume Ratio Calculator

Formula Used:

\[ Icosahedral Edge Length = \frac{12 \times \sqrt{109 - 30 \times \sqrt{5}}}{5 + 7 \times \sqrt{5}} \div Surface To Volume Ratio \]

Icosahedral Edge Length:

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1. What is Icosahedral Edge Length of Triakis Icosahedron?

The Icosahedral Edge Length of Triakis Icosahedron is the length of the line connecting any two adjacent vertices of icosahedron of Triakis Icosahedron. It is a fundamental geometric measurement in this polyhedral structure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Icosahedral Edge Length = \frac{12 \times \sqrt{109 - 30 \times \sqrt{5}}}{5 + 7 \times \sqrt{5}} \div Surface To Volume Ratio \]

Where:

Surface to Volume Ratio - The ratio of total surface area to total volume of the Triakis Icosahedron (1/m)
\(\sqrt{}\) - Square root function

Explanation: This formula calculates the icosahedral edge length based on the surface to volume ratio of the Triakis Icosahedron, incorporating mathematical constants and geometric relationships.

3. Importance of Icosahedral Edge Length Calculation

Details: Calculating the icosahedral edge length is crucial for understanding the geometric properties of Triakis Icosahedron, including its symmetry, volume, surface area, and other dimensional characteristics.

4. Using the Calculator

Tips: Enter the surface to volume ratio in 1/m. The value must be positive and valid for accurate calculation of the icosahedral edge length.

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 isosceles triangular faces.

Q2: Why is the surface to volume ratio important?
A: The surface to volume ratio is important in various applications including material science, chemistry, and physics as it affects properties like reactivity, strength, and heat transfer.

Q3: What are typical values for surface to volume ratio?
A: The surface to volume ratio varies depending on the size and shape of the Triakis Icosahedron, with smaller structures having higher ratios.

Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for calculating the icosahedral edge length of Triakis Icosahedron based on its surface to volume ratio.

Q5: What units are used in this calculation?
A: The surface to volume ratio is in 1/meter (1/m) and the resulting icosahedral edge length is in meters (m).