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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 represents the fundamental measurement that defines the size and proportions of this complex polyhedral structure.
The calculator uses the formula:
Where:
Explanation: The edge length of the stellated octahedron is exactly twice the length of the edges of the tetrahedral peaks attached to the faces of the base octahedron.
Details: Calculating the edge length is essential for determining the overall dimensions, surface area, and volume of the stellated octahedron. It's crucial in geometric modeling, architectural design, and crystallography applications.
Tips: Enter the edge length of peaks in meters. The value must be positive and greater than zero. The calculator will compute the corresponding edge length of the stellated octahedron.
Q1: What is a Stellated Octahedron?
A: A stellated octahedron is a polyhedron formed by attaching tetrahedral pyramids to each face of a regular octahedron, creating a star-like three-dimensional shape.
Q2: Why is the edge length exactly twice the peak edge length?
A: This relationship arises from the geometric construction where each tetrahedral peak extends symmetrically from the base octahedron, creating a precise 2:1 ratio between the overall edge length and the peak edge length.
Q3: What are typical applications of this calculation?
A: This calculation is used in geometric modeling, architectural design, crystal structure analysis, and mathematical education to understand polyhedral properties.
Q4: Are there any limitations to this formula?
A: This formula applies specifically to the regular stellated octahedron where all edges and angles are equal. It assumes perfect geometric construction.
Q5: Can this formula be used for other polyhedra?
A: No, this specific 2:1 ratio applies only to the stellated octahedron. Other polyhedra have different geometric relationships between their components.