Surface To Volume Ratio Of Deltoidal Hexecontahedron Given Short Edge Calculator

Formula Used:

\[ SA:V = \frac{\frac{9}{45}\sqrt{10(157+31\sqrt{5})}}{\sqrt{\frac{370+164\sqrt{5}}{25}}} \times \frac{3(7-\sqrt{5})}{22 \times \text{Short Edge}} \]

Surface to Volume Ratio (SA:V):

Unit Converter ▲

Unit Converter ▼

From:	To:

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

The Surface to Volume Ratio (SA:V) of a Deltoidal Hexecontahedron is a geometric property that represents the relationship between the total surface area and the total volume of this particular polyhedron. It is an important parameter in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the specific formula for Deltoidal Hexecontahedron:

\[ SA:V = \frac{\frac{9}{45}\sqrt{10(157+31\sqrt{5})}}{\sqrt{\frac{370+164\sqrt{5}}{25}}} \times \frac{3(7-\sqrt{5})}{22 \times \text{Short Edge}} \]

Where:

\( \sqrt{} \) — Square root function
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 hexecontahedron and the length of its shortest edge.

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. It helps determine properties like reactivity, heat transfer efficiency, and structural characteristics of three-dimensional shapes.

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 Hexecontahedron?
A: A Deltoidal Hexecontahedron is a Catalan solid with 60 deltoidal faces, 120 edges, and 62 vertices.

Q2: Why is surface to volume ratio important?
A: It indicates how much surface area is available per unit volume, which affects properties like diffusion rates, heat dissipation, and chemical reactivity.

Q3: What units are used for the calculation?
A: The short edge is input in meters (m), and the result 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: Is this formula specific to Deltoidal Hexecontahedron?
A: Yes, this particular formula is derived specifically for calculating the surface to volume ratio of a Deltoidal Hexecontahedron given its short edge length.