Surface to Volume Ratio of Triakis Icosahedron given Midsphere Radius Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = \frac{12\sqrt{109 - 30\sqrt{5}}}{5 + 7\sqrt{5}} \times \frac{1 + \sqrt{5}}{4 \times \text{Midsphere Radius}} \]

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 is an important parameter in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \text{Surface to Volume Ratio} = \frac{12\sqrt{109 - 30\sqrt{5}}}{5 + 7\sqrt{5}} \times \frac{1 + \sqrt{5}}{4 \times \text{Midsphere Radius}} \]

Where:

Midsphere Radius - The radius of the midsphere of the Triakis Icosahedron (in meters)
√5 - Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the surface to volume ratio based on the midsphere radius of the Triakis Icosahedron, incorporating mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and engineering. For polyhedra like the Triakis Icosahedron, this ratio helps in understanding properties related to heat transfer, diffusion, and other surface-dependent phenomena.

4. Using the Calculator

Tips: Enter the midsphere radius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding surface to volume ratio.

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 is the significance of the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron, providing important geometric information about the shape.

Q3: What are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the size of the polyhedron. Smaller polyhedra generally have higher surface to volume ratios.

Q4: Can this calculator handle different units?
A: The calculator uses meters as the unit for input. For other units, appropriate conversion should be applied before input.

Q5: What are the applications of this calculation?
A: This calculation is useful in crystallography, nanotechnology, materials design, and other fields where geometric properties of polyhedra are important.