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Edge Length of Great Dodecahedron given Total Surface Area Calculator

Formula Used:

\[ l_e = \sqrt{\frac{TSA}{15 \times \sqrt{5 - (2 \times \sqrt{5})}}} \]

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1. What is the Edge Length of Great Dodecahedron?

The Edge Length of a Great Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Dodecahedron. It is a fundamental measurement that defines the size and proportions of this geometric shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_e = \sqrt{\frac{TSA}{15 \times \sqrt{5 - (2 \times \sqrt{5})}}} \]

Where:

Explanation: This formula calculates the edge length from the total surface area using the geometric properties specific to the Great Dodecahedron.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the scale and dimensions of a Great Dodecahedron, which is important in various fields including mathematics, architecture, and 3D modeling.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero to compute a valid edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Dodecahedron?
A: A Great Dodecahedron is a Kepler-Poinsot polyhedron with 12 pentagonal faces that intersect each other.

Q2: How is this different from a regular dodecahedron?
A: While both have 12 pentagonal faces, in a Great Dodecahedron the faces intersect, creating a more complex structure.

Q3: What are the applications of this calculation?
A: This calculation is used in geometric modeling, architectural design, and mathematical research involving polyhedra.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Great Dodecahedron due to its unique geometric properties.

Q5: What units should I use for the calculation?
A: Use consistent units (typically meters for length and square meters for area) to ensure accurate results.

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