Surface To Volume Ratio Of Deltoidal Hexecontahedron Given Nonsymmetry Diagonal Calculator

Formula Used:

\[ SA:V = \frac{\frac{9}{45} \times \sqrt{10 \times (157 + (31 \times \sqrt{5}))}}{\sqrt{\frac{370 + (164 \times \sqrt{5})}{25}}} \times \frac{\sqrt{\frac{470 + (156 \times \sqrt{5})}{5}}}{11 \times d_{NonSymmetry}} \]

Surface to Volume Ratio (SA:V):

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

The Surface to Volume Ratio (SA:V) of a Deltoidal Hexecontahedron is a measure that relates the total surface area of the polyhedron to its total volume. It's an important geometric property that indicates how much surface area is available per unit volume of the shape.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( d_{NonSymmetry} \) — NonSymmetry Diagonal of Deltoidal Hexecontahedron (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This complex formula calculates the surface to volume ratio based on the non-symmetry diagonal measurement of the deltoidal hexecontahedron, 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, it helps understand properties like heat transfer efficiency, chemical reactivity, and structural characteristics.

4. Using the Calculator

Tips: Enter the NonSymmetry Diagonal measurement 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 deltoid faces. It's the dual polyhedron of the small rhombicosidodecahedron.

Q2: What does the NonSymmetry Diagonal represent?
A: The NonSymmetry Diagonal is the diagonal that divides the deltoid faces of the Deltoidal Hexecontahedron into two isosceles triangles.

Q3: Why is surface to volume ratio important?
A: It indicates how much surface area is available relative to the volume, which affects properties like diffusion rates, heat transfer, and chemical reactivity.

Q4: What are typical values for this ratio?
A: The ratio depends on the size of the polyhedron. Smaller polyhedra generally have higher surface to volume ratios.

Q5: Can this calculator be used for other polyhedra?
A: No, this specific formula is designed only for the Deltoidal Hexecontahedron given its NonSymmetry Diagonal.