1. What is Edge Length of Gyroelongated Pentagonal Pyramid?

The edge length of a gyroelongated pentagonal pyramid is the length of any edge of this complex polyhedron. It is derived from the total surface area using a specific mathematical formula.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge length (m)
• \( TSA \) — Total surface area (m²)
• \( \sqrt{3} \) — Square root of 3 (≈1.732)
• \( \sqrt{5} \) — Square root of 5 (≈2.236)

Explanation: This formula calculates the edge length by relating it to the total surface area of the gyroelongated pentagonal pyramid through geometric relationships.

3. Importance of Edge Length Calculation

Details: Calculating edge length from surface area is important in geometry and 3D modeling for understanding the scale and proportions of complex polyhedra.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a gyroelongated pentagonal pyramid?
A: It's a Johnson solid formed by attaching a pentagonal pyramid to a pentagonal antiprism.

Q2: Why is the formula so complex?
A: The complexity arises from the irregular geometry and multiple triangular and pentagonal faces of the polyhedron.

Q3: What are typical values for edge length?
A: Edge length depends on the scale of the polyhedron, but typically ranges from centimeters to meters in practical applications.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to gyroelongated pentagonal pyramids due to their unique geometry.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values and proper implementation of the formula.