Home Back

Circumsphere Radius of Great Icosahedron given Volume Calculator

Formula Used:

\[ r_c = \frac{\sqrt{50 + 22\sqrt{5}}}{4} \times \left( \frac{4V}{25 + 9\sqrt{5}} \right)^{1/3} \]

Unit Converter ▲

Unit Converter ▼

From: To:

1. What is the Circumsphere Radius of Great Icosahedron?

The Circumsphere Radius of a Great Icosahedron is the radius of the sphere that contains the polyhedron in such a way that all the vertices lie on the sphere's surface. It is a key geometric property that helps in understanding the spatial dimensions of the Great Icosahedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_c = \frac{\sqrt{50 + 22\sqrt{5}}}{4} \times \left( \frac{4V}{25 + 9\sqrt{5}} \right)^{1/3} \]

Where:

Explanation: This formula calculates the circumsphere radius based on the volume of the Great Icosahedron, incorporating mathematical constants related to its geometry.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is essential for understanding the bounding sphere of the Great Icosahedron, which is important in various geometric analyses, 3D modeling, and computational geometry applications.

4. Using the Calculator

Tips: Enter the volume of the Great Icosahedron in cubic meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Great Icosahedron?
A: The Great Icosahedron is one of the Kepler-Poinsot polyhedra, a non-convex regular polyhedron with 20 triangular faces.

Q2: How is the circumsphere radius different from other radii?
A: The circumsphere radius specifically refers to the radius of the sphere that passes through all vertices of the polyhedron, unlike insphere radius which touches the faces.

Q3: What units should I use for volume input?
A: The calculator expects volume in cubic meters (m³). If your volume is in different units, convert it to cubic meters first.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula is derived for the Great Icosahedron only. Other polyhedra have different formulas for calculating circumsphere radius.

Q5: What is the precision of the calculation?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most geometric calculations and applications.

Circumsphere Radius of Great Icosahedron given Volume Calculator© - All Rights Reserved 2025