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The Mid Ridge Length of Great Icosahedron is the length of any of the edges that starts from the peak vertex and ends on the interior of the pentagon on which each peak of the Great Icosahedron is attached. It is a key geometric parameter in understanding the structure of this complex polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula relates the mid ridge length to the circumsphere radius through the golden ratio and specific geometric constants derived from the icosahedron's structure.
Details: Calculating the mid ridge length is essential for understanding the geometric properties of the Great Icosahedron, including its symmetry, surface area, and volume relationships. It's particularly important in mathematical modeling and 3D geometry applications.
Tips: Enter the circumsphere radius in meters. The value must be positive and non-zero. The calculator will compute the corresponding mid ridge length using the established geometric relationship.
Q1: What is a Great Icosahedron?
A: The Great Icosahedron is one of the four Kepler-Poinsot polyhedra, consisting of 20 triangular faces that intersect each other, creating a complex star polyhedron.
Q2: How is the circumsphere radius defined?
A: The circumsphere radius is the radius of the sphere that contains the Great Icosahedron such that all the peak vertices lie on the sphere's surface.
Q3: What is the significance of the golden ratio in this formula?
A: The golden ratio (1+√5)/2 appears frequently in icosahedral geometry due to the mathematical properties of regular icosahedra and their derivatives.
Q4: Can this formula be used for regular icosahedra?
A: No, this specific formula applies only to the Great Icosahedron, which has different geometric properties than the regular icosahedron.
Q5: What are typical values for mid ridge length?
A: The mid ridge length depends on the size of the polyhedron. For a unit circumsphere radius, the mid ridge length is approximately 0.6498 meters.