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The Circumsphere Radius of a Cuboctahedron is the radius of the sphere that contains the Cuboctahedron in such a way that all the vertices are lying on the sphere. It represents the distance from the center of the Cuboctahedron to any of its vertices.
The calculator uses the formula:
Where:
Explanation: This formula calculates the circumsphere radius based on the lateral surface area of the cuboctahedron, using the mathematical relationship between these geometric properties.
Details: Calculating the circumsphere radius is important in geometry and 3D modeling for understanding the spatial dimensions of a cuboctahedron and its relationship with circumscribed spheres in various applications.
Tips: Enter the lateral surface area in square meters. The value must be positive and valid for accurate calculation of the circumsphere radius.
Q1: What is a Cuboctahedron?
A: A Cuboctahedron is an Archimedean solid with 8 triangular faces and 6 square faces, having 12 identical vertices and 24 identical edges.
Q2: How is Lateral Surface Area different from Total Surface Area?
A: Lateral Surface Area excludes the top and bottom faces, focusing only on the side surfaces of the 3D shape.
Q3: What are typical values for Circumsphere Radius?
A: The circumsphere radius depends on the size of the cuboctahedron. For a unit cuboctahedron (edge length = 1), the circumsphere radius is approximately 1.0 units.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to cuboctahedrons. Other polyhedra have different formulas for calculating circumsphere radius.
Q5: What practical applications use this calculation?
A: This calculation is used in crystallography, molecular modeling, architecture, and various fields of mathematics and engineering where cuboctahedral structures are encountered.