Short Edge Of Deltoidal Hexecontahedron Given Total Surface Area Calculator

Formula Used:

\[ l_{Short} = \frac{3}{22} \times (7 - \sqrt{5}) \times \sqrt{\frac{11 \times TSA}{9 \times \sqrt{10 \times (157 + 31 \times \sqrt{5})}}} \]

Short Edge of Deltoidal Hexecontahedron:

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1. What is the Short Edge of Deltoidal Hexecontahedron?

The Short Edge of Deltoidal Hexecontahedron is the length of the shortest edge of the identical deltoidal faces that make up this complex polyhedron. It is one of the key dimensional parameters that define the geometry of this shape.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ l_{Short} = \frac{3}{22} \times (7 - \sqrt{5}) \times \sqrt{\frac{11 \times TSA}{9 \times \sqrt{10 \times (157 + 31 \times \sqrt{5})}}} \]

Where:

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

Explanation: This formula derives the short edge length from the total surface area using the geometric properties and mathematical relationships specific to the deltoidal hexecontahedron.

3. Importance of Short Edge Calculation

Details: Calculating the short edge is essential for understanding the complete dimensional characteristics of the deltoidal hexecontahedron, which is important in geometric modeling, architectural design, and mathematical research involving complex polyhedra.

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 short edge length of the deltoidal hexecontahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a deltoidal hexecontahedron?
A: A deltoidal hexecontahedron is a Catalan solid with 60 congruent deltoid faces, 120 edges, and 62 vertices.

Q2: Why is this specific formula used?
A: This formula is derived from the geometric relationships between the total surface area and the edge lengths specific to the deltoidal hexecontahedron's symmetric properties.

Q3: What are the units of measurement?
A: The calculator uses meters for length and square meters for area. Ensure consistent units for accurate results.

Q4: Can this calculator handle very large or small values?
A: The calculator can handle a wide range of values, but extremely large or small numbers may be limited by PHP's floating-point precision.

Q5: Is this calculation reversible?
A: Yes, with appropriate mathematical manipulation, the total surface area can be calculated from the short edge length using the inverse relationship.