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The Edge Length of Icosahedron given Space Diagonal is the length of any of edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron, calculated using the space diagonal measurement.
The calculator uses the formula:
Where:
Explanation: This formula calculates the edge length of a regular icosahedron based on its space diagonal measurement, using the mathematical relationship between these two geometric properties.
Details: Calculating the edge length from the space diagonal is important in geometry and 3D modeling for determining the size and proportions of an icosahedron when only the space diagonal measurement is known.
Tips: Enter the space diagonal measurement in meters. The value must be valid (greater than 0).
Q1: What is a regular icosahedron?
A: A regular icosahedron is a polyhedron with 20 equilateral triangular faces, 12 vertices, and 30 edges.
Q2: How is the space diagonal different from face diagonal?
A: The space diagonal connects two vertices that are not on the same face, while a face diagonal connects two non-adjacent vertices on the same face.
Q3: What are typical applications of this calculation?
A: This calculation is used in geometry, 3D modeling, architecture, and various engineering fields where icosahedral structures are employed.
Q4: Are there limitations to this formula?
A: This formula applies only to regular icosahedrons where all edges are equal in length and all faces are equilateral triangles.
Q5: Can this formula be used for other polyhedrons?
A: No, this specific formula is derived for regular icosahedrons only. Other polyhedrons have different mathematical relationships between their space diagonals and edge lengths.