1. What is Circumsphere Radius of Icosahedron?

The Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_c \) — Circumsphere Radius of Icosahedron (m)
• \( d_{Space} \) — Space Diagonal of Icosahedron (m)

Explanation: The circumsphere radius is exactly half the length of the space diagonal of the icosahedron.

3. Importance of Circumsphere Radius Calculation

Details: Calculating the circumsphere radius is important in geometry and 3D modeling for understanding the spatial properties and bounding sphere of an icosahedron.

4. Using the Calculator

Tips: Enter the space diagonal of the icosahedron in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is an icosahedron?
A: An icosahedron is a polyhedron with 20 faces, 30 edges, and 12 vertices. It is one of the five Platonic solids.

Q2: What is the space diagonal of an icosahedron?
A: The space diagonal is the line connecting two vertices that are not on the same face of the icosahedron.

Q3: Are there other ways to calculate circumsphere radius?
A: Yes, the circumsphere radius can also be calculated using the edge length of the icosahedron with the formula: \( r_c = \frac{a}{4} \sqrt{10 + 2\sqrt{5}} \).

Q4: What are typical applications of this calculation?
A: This calculation is used in computer graphics, molecular modeling, and architectural design where icosahedral structures are involved.

Q5: Does this formula work for all regular icosahedrons?
A: Yes, this formula applies to all regular icosahedrons where all edges are equal in length and all faces are equilateral triangles.