NonSymmetry Diagonal Of Deltoidal Hexecontahedron Given Surface To Volume Ratio Calculator

Formula Used:

\[ d_{Non\ Symmetry} = \frac{\sqrt{\frac{470+156\sqrt{5}}{5}}}{11} \times \frac{\frac{9}{45}\sqrt{10(157+31\sqrt{5})}}{AV \times \sqrt{\frac{370+164\sqrt{5}}{25}}} \]

NonSymmetry Diagonal of Deltoidal Hexecontahedron:

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1. What is NonSymmetry Diagonal of Deltoidal Hexecontahedron?

The NonSymmetry Diagonal of Deltoidal Hexecontahedron is the length of the diagonal which divides the deltoid faces of Deltoidal Hexecontahedron into two isosceles triangles. It's an important geometric property of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{Non\ Symmetry} = \frac{\sqrt{\frac{470+156\sqrt{5}}{5}}}{11} \times \frac{\frac{9}{45}\sqrt{10(157+31\sqrt{5})}}{AV \times \sqrt{\frac{370+164\sqrt{5}}{25}}} \]

Where:

\( d_{Non\ Symmetry} \) — NonSymmetry Diagonal of Deltoidal Hexecontahedron (m)
\( AV \) — Surface Area to Volume Ratio of Deltoidal Hexecontahedron (1/m)
\( \sqrt{5} \) — Mathematical constant (approximately 2.23607)

Explanation: This formula calculates the non-symmetry diagonal length based on the surface area to volume ratio of the deltoidal hexecontahedron, incorporating mathematical constants and geometric relationships.

3. Importance of NonSymmetry Diagonal Calculation

Details: Calculating the non-symmetry diagonal is important in geometric analysis, crystallography, and materials science where deltoidal hexecontahedron structures appear. It helps in understanding the spatial properties and symmetry characteristics of this complex polyhedron.

4. Using the Calculator

Tips: Enter the surface area to volume ratio (SA:V) of the deltoidal hexecontahedron in 1/m. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a deltoidal hexecontahedron?
A: A deltoidal hexecontahedron is a Catalan solid with 60 deltoid (kite-shaped) faces. It's the dual polyhedron of the rhombicosidodecahedron.

Q2: How is the surface area to volume ratio measured?
A: The surface area to volume ratio (SA:V) is calculated by dividing the total surface area by the total volume of the polyhedron, expressed in units of 1/length (typically 1/m).

Q3: What are typical values for SA:V of deltoidal hexecontahedron?
A: The SA:V depends on the size of the polyhedron. For a standard deltoidal hexecontahedron with edge length a, the SA:V is approximately 0.2/a.

Q4: What are the applications of this calculation?
A: This calculation is used in crystallography, materials science, architecture, and geometric modeling where deltoidal hexecontahedron structures are encountered.

Q5: Are there limitations to this formula?
A: This formula is specific to the deltoidal hexecontahedron and assumes ideal geometric proportions. For real-world applications, additional factors may need consideration.