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The Circumsphere Radius of a Rhombicosidodecahedron is the radius of the sphere that contains the polyhedron in such a way that all its vertices lie on the sphere's surface. It's a key geometric property of this Archimedean solid.
The calculator uses the formula:
Where:
Explanation: This formula derives the circumsphere radius from the total surface area using the geometric properties specific to the rhombicosidodecahedron.
Details: Calculating the circumsphere radius is essential for understanding the spatial dimensions and bounding sphere of the polyhedron, which has applications in computational geometry, 3D modeling, and mathematical analysis of polyhedral structures.
Tips: Enter the total surface area in square meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is a Rhombicosidodecahedron?
A: A rhombicosidodecahedron is an Archimedean solid with 20 regular triangular faces, 30 square faces, and 12 regular pentagonal faces.
Q2: Why is the circumsphere radius important?
A: It helps determine the smallest sphere that can completely contain the polyhedron, which is useful in collision detection, packaging, and spatial analysis.
Q3: What units should I use for input?
A: The calculator uses square meters for surface area input and returns meters for the circumsphere radius. Ensure consistent units for accurate results.
Q4: Are there limitations to this calculation?
A: This formula assumes a perfect rhombicosidodecahedron shape. For irregular or modified shapes, different calculations would be required.
Q5: Can this calculator handle very large or small values?
A: The calculator can handle a wide range of values, but extremely large or small numbers may be limited by PHP's floating-point precision.