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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 is an important geometric property in three-dimensional space.
The calculator uses the formula:
Where:
Explanation: This formula establishes a direct mathematical relationship between the midsphere radius and the circumsphere radius of a cuboctahedron, using the constant factor 2/√3.
Details: Calculating the circumsphere radius is crucial for understanding the spatial properties of cuboctahedrons, which have applications in crystallography, architecture, and materials science. It helps in determining the bounding sphere that encloses all vertices of the polyhedron.
Tips: Enter the midsphere radius value in meters. The value must be positive and valid. The calculator will automatically compute the corresponding circumsphere radius using the mathematical relationship.
Q1: What is a Cuboctahedron?
A: A cuboctahedron is an Archimedean solid with 8 triangular faces and 6 square faces. It has 12 identical vertices and 24 identical 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 every edge of the polyhedron.
Q3: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to cuboctahedrons. Other polyhedrons have different mathematical relationships between their circumsphere and midsphere radii.
Q4: What are the practical applications of this calculation?
A: This calculation is useful in molecular modeling, crystal structure analysis, and architectural design where cuboctahedral shapes are employed.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect cuboctahedrons. The accuracy depends on the precision of the input midsphere radius value.