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The Circumsphere Radius of Rhombicuboctahedron is the radius of the sphere that contains the Rhombicuboctahedron in such a way that all the vertices are lying on the sphere. It is an important geometric property of this polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula establishes the mathematical relationship between the circumsphere radius and midsphere radius of a rhombicuboctahedron, using square root functions and constants derived from the geometric properties of the shape.
Details: Calculating the circumsphere radius is crucial for understanding the spatial dimensions of the rhombicuboctahedron, its relationship with other geometric properties, and its applications in various fields including architecture, crystallography, and 3D modeling.
Tips: Enter the midsphere radius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding circumsphere radius using the established mathematical relationship.
Q1: What is a rhombicuboctahedron?
A: A rhombicuboctahedron is an Archimedean solid with 8 triangular and 18 square faces, 24 identical vertices, and 48 edges.
Q2: What is the difference between circumsphere and midsphere?
A: The circumsphere passes through all vertices of the polyhedron, while the midsphere is tangent to all edges of the polyhedron.
Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the rhombicuboctahedron as it's derived from its unique geometric properties.
Q4: What are practical applications of this calculation?
A: This calculation is used in architectural design, molecular modeling, game development, and any field dealing with complex 3D geometries.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the perfect rhombicuboctahedron shape.