Surface To Volume Ratio Of Triakis Icosahedron Given Volume Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = \frac{12\sqrt{109-30\sqrt{5}}}{5+7\sqrt{5}} \times \left( \frac{5(5+7\sqrt{5})}{44V} \right)^{1/3} \]

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 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.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Surface to Volume Ratio} = \frac{12\sqrt{109-30\sqrt{5}}}{5+7\sqrt{5}} \times \left( \frac{5(5+7\sqrt{5})}{44V} \right)^{1/3} \]

Where:

\( V \) — Volume of Triakis Icosahedron (m³)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: The formula calculates the surface to volume ratio based on the given volume of the Triakis Icosahedron, using mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Surface to Volume Ratio

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

4. Using the Calculator

Tips: Enter the volume of the Triakis Icosahedron in cubic 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 are typical values for surface to volume ratio?
A: The surface to volume ratio depends on the volume of the polyhedron. Smaller volumes generally yield higher ratios, while larger volumes yield lower ratios.

Q3: What units are used in this calculation?
A: The volume should be in cubic meters (m³), and the resulting surface to volume ratio will be in inverse meters (m⁻¹).

Q4: Are there limitations to this formula?
A: This formula is specifically derived for perfect Triakis Icosahedrons and assumes ideal geometric properties.

Q5: Can this calculator handle very small or very large volumes?
A: The calculator can handle a wide range of volume values, but extremely small values close to zero or extremely large values may affect computational precision.