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The Edge Length of Great Icosahedron is the distance between any pair of adjacent peak vertices of the Great Icosahedron. It is a fundamental geometric measurement that defines the size and proportions of this complex polyhedron.
The calculator uses the mathematical formula:
Where:
Explanation: This formula establishes the precise mathematical relationship between the mid ridge length and the edge length in a Great Icosahedron, utilizing the golden ratio properties inherent in its geometry.
Details: The Great Icosahedron is a complex star polyhedron with 20 triangular faces. Its geometry involves the golden ratio (φ = (1+√5)/2), which appears in the relationship between various edge measurements including the mid ridge length and edge length.
Tips: Enter the mid ridge length in meters. The value must be positive and greater than zero. The calculator will compute the corresponding edge length based on the geometric relationship.
Q1: What is a Great Icosahedron?
A: The Great Icosahedron is one of the four Kepler-Poinsot polyhedra, a star polyhedron with 20 intersecting triangular faces.
Q2: How is this different from a regular icosahedron?
A: While both have 20 triangular faces, the Great Icosahedron is a star polyhedron with self-intersecting faces, creating a more complex structure.
Q3: What practical applications does this calculation have?
A: This calculation is primarily used in mathematical geometry, architectural design, and 3D modeling where precise geometric relationships are required.
Q4: Why does the formula include √5?
A: The square root of 5 appears because the geometry of the Great Icosahedron is fundamentally related to the golden ratio, and φ = (1+√5)/2.
Q5: Can this formula be used in reverse?
A: Yes, the formula can be rearranged to calculate mid ridge length from edge length: Mid Ridge Length = Edge Length × (1+√5)/2.