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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 total surface area by utilizing the geometric properties of a regular icosahedron.
Details: Calculating the circumsphere radius is important in geometry, 3D modeling, and various engineering applications where precise spatial relationships of icosahedral structures need to be determined.
Tips: Enter the total surface area of the icosahedron in square meters. The value must be positive and greater than zero for accurate calculation.
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 this formula derived?
A: The formula is derived from the relationship between the circumsphere radius and the surface area through the side length of the icosahedron's triangular faces.
Q3: What are typical applications of this calculation?
A: This calculation is used in molecular modeling, architectural design, game development, and any field dealing with icosahedral symmetry.
Q4: Can this calculator handle different units?
A: The calculator expects input in square meters and outputs in meters. For other units, convert your measurements accordingly before calculation.
Q5: What is the precision of the calculation?
A: The calculator provides results with 6 decimal places precision, which is suitable for most practical applications.