Symmetry Diagonal Of Deltoidal Hexecontahedron Given Total Surface Area Calculator

Formula Used:

\[ d_{Symmetry} = \sqrt{\frac{5-\sqrt{5}}{20}} \times \sqrt{\frac{11 \times TSA}{\sqrt{10 \times (157 + 31 \times \sqrt{5})}}} \]

Symmetry Diagonal of Deltoidal Hexecontahedron:

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1. What is Symmetry Diagonal of Deltoidal Hexecontahedron?

The Symmetry Diagonal of Deltoidal Hexecontahedron is the diagonal which cuts the deltoid faces of Deltoidal Hexecontahedron into two equal halves. It is an important geometric property of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{Symmetry} = \sqrt{\frac{5-\sqrt{5}}{20}} \times \sqrt{\frac{11 \times TSA}{\sqrt{10 \times (157 + 31 \times \sqrt{5})}}} \]

Where:

\( d_{Symmetry} \) — Symmetry Diagonal of Deltoidal Hexecontahedron (m)
\( TSA \) — Total Surface Area of Deltoidal Hexecontahedron (m²)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the symmetry diagonal based on the total surface area of the deltoidal hexecontahedron, incorporating mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Symmetry Diagonal Calculation

Details: Calculating the symmetry diagonal is crucial for understanding the geometric properties of deltoidal hexecontahedron, including its symmetry characteristics and spatial relationships between different parts of the polyhedron.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and valid. The calculator will compute the corresponding symmetry diagonal of the deltoidal hexecontahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a deltoidal hexecontahedron?
A: A deltoidal hexecontahedron is a polyhedron with 60 deltoid (kite-shaped) faces. It is one of the Catalan solids.

Q2: How is symmetry diagonal different from other diagonals?
A: The symmetry diagonal specifically refers to the diagonal that bisects the deltoid faces symmetrically, creating two equal halves.

Q3: What are the applications of this calculation?
A: This calculation is used in geometry, crystallography, architecture, and various fields that study polyhedral structures and their properties.

Q4: Are there limitations to this formula?
A: This formula is specifically designed for the deltoidal hexecontahedron and assumes a perfect geometric shape with ideal proportions.

Q5: Can this calculator handle different units?
A: The calculator uses square meters for surface area and meters for the result. For other units, appropriate conversion should be applied before and after calculation.