Surface to Volume Ratio of Deltoidal Icositetrahedron given Volume Calculator

Formula Used:

\[ SA:V = \frac{6\sqrt{61+38\sqrt{2}}}{\sqrt{292+206\sqrt{2}}} \times \left( \frac{2\sqrt{292+206\sqrt{2}}}{7V} \right)^{\frac{1}{3}} \]

Surface to Volume Ratio (SA:V):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Surface to Volume Ratio of Deltoidal Icositetrahedron?

The Surface to Volume Ratio (SA:V) of a Deltoidal Icositetrahedron is a measure that indicates what part of or fraction of the total volume is represented by the total surface area. It's an important geometric property that relates the external surface area to the internal volume of this specific polyhedron.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ SA:V = \frac{6\sqrt{61+38\sqrt{2}}}{\sqrt{292+206\sqrt{2}}} \times \left( \frac{2\sqrt{292+206\sqrt{2}}}{7V} \right)^{\frac{1}{3}} \]

Where:

\( V \) — Volume of Deltoidal Icositetrahedron (m³)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
The formula combines square root functions and cube roots to calculate the ratio

Explanation: The formula accounts for the complex geometric relationships in a Deltoidal Icositetrahedron, relating its surface area to volume through mathematical constants and the given volume.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and physics. For polyhedra, it helps understand properties like heat transfer, diffusion rates, and structural efficiency.

4. Using the Calculator

Tips: Enter the volume of the Deltoidal Icositetrahedron in cubic meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Icositetrahedron?
A: A Deltoidal Icositetrahedron is a Catalan solid with 24 deltoid (kite-shaped) faces. It's the dual polyhedron of the rhombicuboctahedron.

Q2: What units are used in this calculation?
A: The volume input should be in cubic meters (m³), and the resulting surface to volume ratio is in inverse meters (m⁻¹).

Q3: Why is the surface to volume ratio important?
A: This ratio is significant in many scientific applications, including determining reaction rates, heat dissipation, and material properties in various engineering contexts.

Q4: 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 approaching zero may result in computational limitations.

Q5: Is this formula specific to Deltoidal Icositetrahedron?
A: Yes, this particular formula is specifically derived for calculating the surface to volume ratio of a Deltoidal Icositetrahedron given its volume.