Formula Used:
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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 sphere's surface. It is a key geometric property that helps in understanding the spatial dimensions of the Great Icosahedron.
The calculator uses the formula:
Where:
Explanation: This formula calculates the circumsphere radius based on the volume of the Great Icosahedron, incorporating mathematical constants related to its geometry.
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.
Tips: Enter the volume of the Great Icosahedron in cubic meters. The value must be positive and greater than zero for accurate calculation.
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.