Long Edge Of Deltoidal Hexecontahedron Given Total Surface Area Calculator

Formula Used:

\[ Long Edge = \sqrt{\frac{11 \times Total Surface Area}{9 \times \sqrt{10 \times (157 + 31 \times \sqrt{5})}}} \]

Long Edge Of Deltoidal Hexecontahedron:

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1. What Is The Long Edge Of Deltoidal Hexecontahedron?

The Long Edge of Deltoidal Hexecontahedron is the length of the longest edge of the identical deltoidal faces of Deltoidal Hexecontahedron. It is a key geometric parameter in understanding the shape and properties of this polyhedron.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ Long Edge = \sqrt{\frac{11 \times Total Surface Area}{9 \times \sqrt{10 \times (157 + 31 \times \sqrt{5})}}} \]

Where:

\( Total Surface Area \) — The total surface area of the Deltoidal Hexecontahedron (m²)

Explanation: This formula calculates the long edge length based on the total surface area of the polyhedron, incorporating mathematical constants and geometric relationships specific to the Deltoidal Hexecontahedron.

3. Importance Of Long Edge Calculation

Details: Calculating the long edge is essential for geometric analysis, architectural applications, and understanding the spatial properties of the Deltoidal Hexecontahedron in mathematical and engineering contexts.

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 long edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Hexecontahedron?
A: A Deltoidal Hexecontahedron is a polyhedron with 60 deltoidal (kite-shaped) faces. It is a Catalan solid, the dual of the rhombicosidodecahedron.

Q2: Why is this specific formula used?
A: The formula derives from the geometric properties and mathematical relationships specific to the Deltoidal Hexecontahedron, ensuring accurate calculation of the long edge from the total surface area.

Q3: What units should be used?
A: The total surface area should be in square meters, and the resulting long edge will be in meters. Consistent units are crucial for accurate results.

Q4: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for the Deltoidal Hexecontahedron. Other polyhedra have different geometric properties and require different formulas.

Q5: What if I have the short edge instead?
A: This calculator requires the total surface area. If you have the short edge, you would need a different formula or calculator to find the long edge or total surface area first.