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The edge length of a gyroelongated pentagonal pyramid is the measurement of any edge of this complex polyhedron. It's a fundamental geometric property that helps define the overall size and proportions of the shape.
The calculator uses the mathematical formula:
Where:
Explanation: This formula derives from the geometric properties of pentagons and the specific construction of gyroelongated pyramids, incorporating the golden ratio relationships inherent in pentagonal geometry.
Details: Calculating the edge length is essential for understanding the scale of the polyhedron, determining surface area and volume, and for practical applications in architecture, molecular modeling, and mathematical research involving complex polyhedra.
Tips: Enter the height of the gyroelongated pentagonal pyramid in meters. The value must be positive and non-zero. The calculator will compute the corresponding edge length.
Q1: What is a gyroelongated pentagonal pyramid?
A: It's a Johnson solid created by attaching a pentagonal antiprism to a pentagonal pyramid, resulting in a complex polyhedron with triangular and pentagonal faces.
Q2: Why is the formula so complex?
A: The complexity arises from the intricate geometry involving pentagonal symmetry and the golden ratio, which requires square roots and fractional expressions to accurately represent the mathematical relationships.
Q3: What are practical applications of this calculation?
A: Applications include architectural design, molecular modeling of complex structures, mathematical research, and computer graphics modeling of complex shapes.
Q4: How accurate is this calculator?
A: The calculator provides results with high precision (up to 12 decimal places), making it suitable for both educational and professional applications.
Q5: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to gyroelongated pentagonal pyramids. Other polyhedra have different geometric relationships and require different formulas.