Edge Length of Great Icosahedron given Long Ridge Length Calculator

Formula Used:

\[ Edge\ Length = \frac{10 \times Long\ Ridge\ Length}{\sqrt{2} \times (5 + 3\sqrt{5})} \]

Edge Length of Great Icosahedron:

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1. What is Edge Length of Great Icosahedron?

The Edge Length of Great Icosahedron is the distance between any pair of adjacent peak vertices of the Great Icosahedron. It is a fundamental geometric measurement used in polyhedral geometry and three-dimensional shape analysis.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ Edge\ Length = \frac{10 \times Long\ Ridge\ Length}{\sqrt{2} \times (5 + 3\sqrt{5})} \]

Where:

Long Ridge Length — The length of edges connecting peak vertex and adjacent vertex
√2 — Square root of 2 (approximately 1.4142)
√5 — Square root of 5 (approximately 2.2361)

Explanation: This formula derives from the geometric relationships within the Great Icosahedron structure, using mathematical constants and ratios specific to this polyhedron.

3. Importance of Edge Length Calculation

Details: Calculating edge length is essential for understanding the geometric properties, surface area, volume, and spatial relationships of the Great Icosahedron in mathematical and engineering applications.

4. Using the Calculator

Tips: Enter the Long Ridge Length in meters. The value must be positive and valid. The calculator will compute the corresponding Edge Length of the Great Icosahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Icosahedron?
A: The Great Icosahedron is one of the four regular star polyhedra, consisting of 20 triangular faces that intersect each other.

Q2: How is this different from a regular icosahedron?
A: While both have triangular faces, the Great Icosahedron is a star polyhedron with self-intersecting faces, unlike the convex regular icosahedron.

Q3: What are practical applications of this calculation?
A: This calculation is used in geometric modeling, architectural design, molecular structures, and mathematical research involving polyhedral geometry.

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

Q5: What precision should I expect from the calculation?
A: The calculator provides results with 6 decimal places precision, suitable for most mathematical and engineering applications.