Total Surface Area Of Deltoidal Hexecontahedron Given Symmetry Diagonal Calculator

Formula Used:

\[ TSA = \frac{9}{11} \times \sqrt{10 \times (157 + (31 \times \sqrt{5})))} \times \left( \frac{d_{Symmetry}}{3 \times \sqrt{\frac{5 - \sqrt{5}}{20}}} \right)^2 \]

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 a Deltoidal Hexecontahedron refers to the total area covered by all the faces of this polyhedron. It is a measure of the complete outer surface of the shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{9}{11} \times \sqrt{10 \times (157 + (31 \times \sqrt{5})))} \times \left( \frac{d_{Symmetry}}{3 \times \sqrt{\frac{5 - \sqrt{5}}{20}}} \right)^2 \]

Where:

\( TSA \) — Total Surface Area of Deltoidal Hexecontahedron (m²)
\( d_{Symmetry} \) — Symmetry Diagonal of Deltoidal Hexecontahedron (m)

Explanation: The formula calculates the total surface area based on the symmetry diagonal measurement of the deltoidal hexecontahedron.

3. Importance of Surface Area Calculation

Details: Calculating the surface area is important in various fields including geometry, material science, and engineering where surface properties and coverage need to be determined.

4. Using the Calculator

Tips: Enter the symmetry diagonal value in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

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

Q2: What is the symmetry diagonal?
A: The symmetry diagonal is the diagonal that cuts the deltoid faces of the Deltoidal Hexecontahedron into two equal halves.

Q3: What units should I use for input?
A: The calculator expects the symmetry diagonal input in meters (m), and returns the surface area in square meters (m²).

Q4: Can this calculator handle very large or very small values?
A: Yes, the calculator can handle a wide range of positive values, though extremely large or small values may be limited by computational precision.

Q5: Is this formula specific to Deltoidal Hexecontahedron?
A: Yes, this formula is specifically derived for calculating the total surface area of a Deltoidal Hexecontahedron given its symmetry diagonal.