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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 surface of the sphere. It is a key geometric property of this complex polyhedral shape.
The calculator uses the mathematical formula:
Where:
Explanation: This formula calculates the radius of the circumscribed sphere based on the edge length of the Great Icosahedron, incorporating the mathematical constant √5 which is characteristic of icosahedral geometry.
Details: Calculating the circumsphere radius is essential for understanding the spatial dimensions of the Great Icosahedron, for geometric modeling applications, and for determining how this polyhedron fits within spherical boundaries in various mathematical and engineering contexts.
Tips: Enter the edge length of the Great Icosahedron in meters. The value must be positive and greater than zero. The calculator will compute the corresponding circumsphere radius.
Q1: What is a Great Icosahedron?
A: The Great Icosahedron is one of the four Kepler-Poinsot polyhedra, a non-convex polyhedron with 20 triangular faces that intersect each other.
Q2: How is this different from a regular icosahedron?
A: While both have icosahedral symmetry, the Great Icosahedron is star-shaped (non-convex) with self-intersecting faces, whereas a regular icosahedron is convex.
Q3: What are practical applications of this calculation?
A: This calculation is used in geometric modeling, architectural design, molecular modeling (particularly in virology), and mathematical research involving polyhedral structures.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Great Icosahedron. Other polyhedra have different formulas for calculating their circumsphere radii.
Q5: What precision does the calculator provide?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most mathematical and engineering applications.