Total Surface Area of Deltoidal Hexecontahedron given NonSymmetry Diagonal Calculator

Formula Used:

\[ TSA = \frac{9}{11} \times \sqrt{10 \times (157 + 31 \times \sqrt{5})} \times \frac{(11 \times d_{Non\ Symmetry})^2}{\frac{470 + 156 \times \sqrt{5}}{5}} \]

Total Surface Area of Deltoidal Hexecontahedron:

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1. What is the Total Surface Area of Deltoidal Hexecontahedron?

The Total Surface Area of Deltoidal Hexecontahedron is the amount or quantity of two dimensional space covered by the surface of Deltoidal Hexecontahedron. It is an important geometric property used in various mathematical and engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{9}{11} \times \sqrt{10 \times (157 + 31 \times \sqrt{5})} \times \frac{(11 \times d_{Non\ Symmetry})^2}{\frac{470 + 156 \times \sqrt{5}}{5}} \]

Where:

\( TSA \) — Total Surface Area of Deltoidal Hexecontahedron (m²)
\( d_{Non\ Symmetry} \) — NonSymmetry Diagonal of Deltoidal Hexecontahedron (m)
\( \sqrt{} \) — Square root function

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

3. Importance of Surface Area Calculation

Details: Calculating the surface area of geometric solids is crucial in various fields including architecture, material science, and engineering design. It helps in determining material requirements, heat transfer properties, and structural characteristics.

4. Using the Calculator

Tips: Enter the NonSymmetry Diagonal value in meters. The value must be positive and greater than zero. The calculator will compute the total surface area using the specialized formula for deltoidal hexecontahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Hexecontahedron?
A: A Deltoidal Hexecontahedron is a Catalan solid with 60 deltoid faces. It is the dual polyhedron of the rhombicosidodecahedron.

Q2: What units should I use for input?
A: The calculator expects the NonSymmetry Diagonal input in meters, and returns the surface area in square meters.

Q3: How accurate is this calculation?
A: The calculation uses precise mathematical formulas and provides results with high accuracy, typically rounded to 6 decimal places.

Q4: Can this calculator handle very large or small values?
A: Yes, the calculator can handle a wide range of values as long as they are positive numbers.

Q5: What are the practical applications of this calculation?
A: This calculation is useful in geometric modeling, architectural design, material estimation, and educational purposes involving advanced polyhedra.