Home
Back
Formula Used:
| From: | To: |
The circumsphere radius of an icosahedron is the radius of the sphere that contains the icosahedron in such a way that all the vertices are lying on the sphere. It represents the distance from the center of the icosahedron to any of its vertices.
The calculator uses the formula:
Where:
Explanation: This formula derives the circumsphere radius from the volume of a regular icosahedron, using the mathematical relationship between these geometric properties.
Details: Calculating the circumsphere radius is important in geometry, 3D modeling, and various engineering applications where understanding the spatial dimensions and bounding sphere of an icosahedral structure is required.
Tips: Enter the volume of the icosahedron in cubic meters. The volume must be a positive value greater than zero.
Q1: What is a regular icosahedron?
A: A regular icosahedron is a polyhedron with 20 equilateral triangular faces, 12 vertices, and 30 edges. It is one of the five Platonic solids.
Q2: How is the circumsphere radius related to other icosahedron measurements?
A: The circumsphere radius can also be calculated from the edge length (a) using the formula: \( r_c = \frac{a}{4} \sqrt{10 + 2\sqrt{5}} \).
Q3: What are typical applications of icosahedron geometry?
A: Icosahedral structures appear in various fields including architecture, chemistry (fullerenes), virology (viral capsids), and geodesic dome design.
Q4: Can this calculator handle very large or very small volumes?
A: The calculator can handle a wide range of volume values, but extremely large or small values may be limited by PHP's floating-point precision.
Q5: Is the circumsphere radius always larger than the insphere radius?
A: Yes, for any convex polyhedron, the circumsphere radius (touching vertices) is always greater than or equal to the insphere radius (touching faces).