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The Short Ridge Length of Great Icosahedron is defined as the maximum vertical distance between the finished bottom level and the finished top height directly above of Great Icosahedron. It is an important geometric measurement in the study of polyhedral structures.
The calculator uses the formula:
Where:
Explanation: This formula calculates the short ridge length based on the circumsphere radius of the Great Icosahedron, using mathematical constants and square root functions.
Details: Accurate calculation of ridge lengths is crucial for geometric modeling, architectural design, and understanding the structural properties of polyhedral shapes in mathematics and engineering applications.
Tips: Enter the circumsphere radius in meters. The value must be positive and greater than zero. The calculator will compute the corresponding short ridge length of the Great Icosahedron.
Q1: What is a Great Icosahedron?
A: The Great Icosahedron is one of the four Kepler-Poinsot polyhedra, which are regular star polyhedra. It has 20 triangular faces that intersect each other.
Q2: How is circumsphere radius defined?
A: The circumsphere radius is the radius of the sphere that contains the Great Icosahedron such that all vertices lie on the sphere's surface.
Q3: What are typical values for these measurements?
A: The values depend on the specific size of the polyhedron. For standard reference polyhedra, circumsphere radii typically range from centimeters to meters in practical applications.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Great Icosahedron. Other polyhedra have different geometric relationships and require different formulas.
Q5: What precision should I expect from the calculation?
A: The calculator provides results with 6 decimal places precision, which is sufficient for most mathematical and engineering applications involving polyhedral geometry.