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The Circumsphere Radius of an Octahedron is the radius of the sphere that contains the octahedron in such a way that all the vertices are lying on the sphere. It represents the distance from the center of the octahedron to any of its vertices.
The calculator uses the formula:
Where:
Explanation: This formula establishes the precise mathematical relationship between the circumsphere radius and midsphere radius of a regular octahedron.
Details: Calculating the circumsphere radius is crucial in geometry and 3D modeling for determining the spatial requirements of octahedral structures, understanding their geometric properties, and applications in crystallography and molecular modeling.
Tips: Enter the midsphere radius value in meters. The value must be positive and greater than zero. The calculator will automatically compute the corresponding circumsphere radius.
Q1: What is a regular octahedron?
A: A regular octahedron is a polyhedron with eight equilateral triangular faces, twelve edges, and six vertices. It is one of the five Platonic solids.
Q2: What is the difference between circumsphere and midsphere?
A: The circumsphere passes through all vertices of the octahedron, while the midsphere is tangent to all edges of the octahedron.
Q3: Can this formula be used for irregular octahedrons?
A: No, this specific formula applies only to regular octahedrons where all edges are equal and all faces are equilateral triangles.
Q4: What are practical applications of this calculation?
A: This calculation is used in crystallography, molecular geometry, 3D computer graphics, architectural design, and various engineering applications involving octahedral structures.
Q5: How accurate is the calculation?
A: The calculation is mathematically exact for regular octahedrons, as it's derived from the geometric properties of the shape.