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The Edge Length of Stellated Octahedron is the distance between any pair of adjacent peak vertices of the Stellated Octahedron. It is a fundamental geometric measurement that defines the size and proportions of this polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula establishes the mathematical relationship between the edge length of a stellated octahedron and the radius of its circumscribed sphere.
Details: Calculating the edge length is essential for understanding the geometric properties, surface area, volume, and spatial characteristics of the stellated octahedron in various mathematical and engineering applications.
Tips: Enter the circumsphere radius in meters. The value must be positive and valid for accurate calculation.
Q1: What is a Stellated Octahedron?
A: A stellated octahedron is a polyhedron formed by extending the faces of a regular octahedron until they meet again, creating a star-like shape with triangular pyramids on each face.
Q2: What is the Circumsphere Radius?
A: The circumsphere radius is the radius of the sphere that contains the stellated octahedron such that all its vertices lie on the surface of the sphere.
Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the stellated octahedron. Different polyhedra have different relationships between edge length and circumsphere radius.
Q4: What are practical applications of this calculation?
A: This calculation is used in geometry, architecture, crystal structures, and 3D modeling where stellated octahedron shapes are employed.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a perfect stellated octahedron, assuming precise input values and proper geometric construction.