1. What is the 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 property that defines the size and proportions of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( Circumsphere Radius \) — Radius of the sphere that contains the Great Icosahedron
• \( \sqrt{} \) — Square root function

Explanation: This formula establishes the precise relationship between the circumsphere radius and the edge length of a Great Icosahedron, incorporating the mathematical constant √5.

3. Importance of Edge Length Calculation

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

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and greater than zero to obtain a valid edge length calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Icosahedron?
A: The Great Icosahedron is one of the four Kepler-Poinsot polyhedra, featuring 20 triangular faces that intersect each other, creating a complex star polyhedron.

Q2: How is this different from a regular icosahedron?
A: Unlike the regular icosahedron where faces don't intersect, the Great Icosahedron has self-intersecting faces, creating a more complex geometric structure.

Q3: What practical applications does this calculation have?
A: This calculation is used in mathematical modeling, architectural design, crystal structure analysis, and geometric art applications.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Great Icosahedron. Other polyhedra have different mathematical relationships between edge length and circumsphere radius.

Q5: What is the significance of the √5 constant in the formula?
A: The √5 constant appears frequently in formulas related to icosahedral symmetry and is fundamental to the geometry of pentagonal and icosahedral structures.