Surface To Volume Ratio Of Deltoidal Icositetrahedron Given Short Edge Calculator

Formula Used:

\[ SA:V = \frac{6\sqrt{61+38\sqrt{2}}}{\sqrt{292+206\sqrt{2}}} \times \frac{4+\sqrt{2}}{7 \times \text{Short Edge}} \]

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 represents the relationship between its total surface area and its total volume. It indicates how much surface area is available per unit volume of this specific polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ SA:V = \frac{6\sqrt{61+38\sqrt{2}}}{\sqrt{292+206\sqrt{2}}} \times \frac{4+\sqrt{2}}{7 \times \text{Short Edge}} \]

Where:

\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
Short Edge — Length of the shortest edge of the deltoidal faces (in meters)

Explanation: This formula calculates the surface to volume ratio based on the geometric properties of the Deltoidal Icositetrahedron and its shortest edge measurement.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various applications including material science, chemistry, and physics. It helps determine properties like reactivity, heat transfer efficiency, and diffusion rates in polyhedral structures.

4. Using the Calculator

Tips: Enter the length of the short edge in meters. The value must be positive and greater than zero. The calculator will compute the surface to volume ratio in reciprocal meters (m⁻¹).

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, 26 vertices, and 48 edges.

Q2: Why is the surface to volume ratio important?
A: It helps understand how the shape's properties change with size, particularly in areas like catalysis, heat transfer, and biological systems.

Q3: What units are used for the calculation?
A: The short edge is measured in meters (m), and the surface to volume ratio is given in reciprocal meters (m⁻¹).

Q4: Can this calculator handle very small or large values?
A: Yes, as long as the input is a positive number greater than zero, the calculator can handle a wide range of values.

Q5: How accurate is the calculation?
A: The calculation uses precise mathematical constants and provides results with high accuracy up to 15 decimal places.