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The Insphere Radius of an Icosahedron is the radius of the sphere that is contained within the Icosahedron such that it touches all the faces of the polyhedron. This sphere is tangent to each face of the Icosahedron at exactly one point.
The calculator uses the formula:
Where:
Explanation: This formula calculates the insphere radius based on the lateral surface area of a regular icosahedron, using mathematical constants and geometric relationships specific to this polyhedron.
Details: Calculating the insphere radius is important in geometry and 3D modeling as it helps determine the maximum size of a sphere that can fit perfectly inside an icosahedron without intersecting any of its faces.
Tips: Enter the lateral surface area of the icosahedron in square meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is a regular icosahedron?
A: A regular icosahedron is a convex polyhedron with 20 identical equilateral triangular faces, 30 edges, and 12 vertices.
Q2: How is lateral surface area different from total surface area?
A: Lateral surface area excludes the base area(s) of a 3D shape, while total surface area includes all faces of the object.
Q3: Can this formula be used for irregular icosahedrons?
A: No, this formula is specifically designed for regular icosahedrons where all faces are identical equilateral triangles.
Q4: What are practical applications of this calculation?
A: This calculation is useful in crystallography, molecular modeling, architecture, and any field dealing with regular polyhedrons and sphere packing.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular icosahedrons, with accuracy depending on the precision of the input value.