Total Surface Area Of Deltoidal Hexecontahedron Calculator

Deltoidal Hexecontahedron Formula:

\[ TSA = \frac{9}{11} \times \sqrt{10 \times (157 + (31 \times \sqrt{5})))} \times le_{Long}^2 \]

Total Surface Area of Deltoidal Hexecontahedron:

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1. What is the Deltoidal Hexecontahedron?

The Deltoidal Hexecontahedron is a Catalan solid with 60 deltoidal (kite-shaped) faces. It is the dual polyhedron of the rhombicosidodecahedron and has interesting geometric properties.

2. How Does the Calculator Work?

The calculator uses the Deltoidal Hexecontahedron surface area formula:

\[ TSA = \frac{9}{11} \times \sqrt{10 \times (157 + (31 \times \sqrt{5})))} \times le_{Long}^2 \]

Where:

\( TSA \) — Total Surface Area of Deltoidal Hexecontahedron (m²)
\( le_{Long} \) — Long Edge of Deltoidal Hexecontahedron (m)
\( \sqrt{} \) — Square root function

Explanation: The formula calculates the total surface area based on the length of the long edge of the deltoidal faces, incorporating mathematical constants and square roots for precise computation.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of geometric solids is essential in various fields including architecture, materials science, and 3D modeling. For the Deltoidal Hexecontahedron, this calculation helps in understanding its spatial properties and potential applications.

4. Using the Calculator

Tips: Enter the length of the long edge in meters. The value must be positive and greater than zero. The calculator will compute the total surface area using the precise mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Hexecontahedron?
A: It's a Catalan solid with 60 identical deltoidal (kite-shaped) faces, 120 edges, and 62 vertices.

Q2: What are the practical applications of this calculation?
A: This calculation is useful in crystallography, architectural design, and mathematical modeling of complex geometric structures.

Q3: How accurate is this formula?
A: The formula provides mathematically exact results for the surface area calculation of a perfect Deltoidal Hexecontahedron.

Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit, but you can convert from other units by providing the equivalent value in meters.

Q5: What is the relationship between edge length and surface area?
A: The surface area increases with the square of the edge length, following the formula TSA ∝ le².