1. What is Circumsphere Radius of Great Icosahedron?

The Circumsphere Radius of Great Icosahedron is the radius of the sphere that contains the Great Icosahedron in such a way that all the peak vertices are lying on the sphere. It is an important geometric property of this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumsphere Radius of Great Icosahedron (m)
• \( l_{Ridge(Mid)} \) — Mid Ridge Length of Great Icosahedron (m)
• \( \sqrt{5} \) — Mathematical constant (approximately 2.23607)

Explanation: This formula calculates the circumsphere radius based on the mid ridge length of the Great Icosahedron, incorporating the golden ratio and other geometric properties specific to this shape.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is essential for understanding the spatial dimensions and geometric properties of the Great Icosahedron. It helps in various applications including 3D modeling, architectural design, and mathematical analysis of polyhedra.

4. Using the Calculator

Tips: Enter the Mid Ridge Length of the Great Icosahedron in meters. The value must be positive and greater than zero. The calculator will compute the corresponding circumsphere radius.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Icosahedron?
A: The Great Icosahedron is one of the four Kepler-Poinsot polyhedra. It is a non-convex polyhedron with 20 triangular faces that intersect each other.

Q2: How is the Mid Ridge Length defined?
A: The Mid Ridge Length is the length of any of the edges that starts from the peak vertex and ends on the interior of the pentagon on which each peak of the Great Icosahedron is attached.

Q3: What are typical values for Circumsphere Radius?
A: The circumsphere radius depends on the specific dimensions of the Great Icosahedron. For standard configurations, it typically ranges from a few centimeters to several meters, depending on the scale of the polyhedron.

Q4: Can this calculator be used for other polyhedra?
A: No, this specific formula and calculator are designed specifically for the Great Icosahedron. Other polyhedra have different formulas for calculating their circumsphere radii.

Q5: What precision should I expect from the calculation?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most practical applications involving geometric calculations.