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Edge Length of Gyroelongated Square Dipyramid given Height Calculator

Formula Used:

\[ Edge Length = \frac{Height}{\sqrt{1 - \frac{1}{2 + \sqrt{2}}} + \sqrt{2}} \]

m

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1. What is the Edge Length of Gyroelongated Square Dipyramid?

The edge length of a Gyroelongated Square Dipyramid is the length of any edge of this polyhedron. It is a fundamental measurement that determines the overall size and proportions of this geometric shape.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ Edge Length = \frac{Height}{\sqrt{1 - \frac{1}{2 + \sqrt{2}}} + \sqrt{2}} \]

Where:

Explanation: This formula calculates the edge length based on the given height of the polyhedron, using square root functions and mathematical constants.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for understanding the geometric properties, volume, surface area, and other dimensional characteristics of the Gyroelongated Square Dipyramid.

4. Using the Calculator

Tips: Enter the height of the Gyroelongated Square Dipyramid in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a Gyroelongated Square Dipyramid?
A: A Gyroelongated Square Dipyramid is a polyhedron formed by attaching two square pyramids to a square antiprism, creating a complex geometric shape with triangular faces.

Q2: What are the applications of this calculation?
A: This calculation is useful in geometry, architecture, 3D modeling, and mathematical research involving polyhedral structures.

Q3: How accurate is this formula?
A: The formula is mathematically precise and provides exact results based on the geometric properties of the Gyroelongated Square Dipyramid.

Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters before calculation.

Q5: What if I get an error in calculation?
A: Ensure you've entered a valid positive number for the height. The calculator will not accept negative values or zero.

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